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How can I buy cocaine online in Miskolc

Activities by an organized crime group involving the illegal entry, transit or residence of migrants for a financial or material benefit. The production, transport, storage and sale of goods that are fraudulently mislabeled or fraudulent imitations of registered brands. The illicit transport, handling and sale of excise consumer goods despite a ban or outside a legal market. Excludes oil and counterfeits. The illicit trade and possession of species covered by CITES convention, and other species protected under national law. The poaching, illicit trade in and possession of species covered by CITES and other species protected by national law. Includes IUU fishing. The illicit extraction, smuggling, mingling, bunkering or mining of natural resources and the illicit trade of such commodities. The production, distribution and sale of heroin. Consumption of the drug is considered in determining the reach of the criminal market. The production, distribution and sale of cocaine and its derivatives. Consumption is considered in determining the reach of the market. The illicit cultivation, distribution and sale of cannabis oil, resin, herb or leaves. Consumption is used to determine the market's reach. The production, distribution and sale of synthetic drugs. Organized crime that results in a monetary loss via financial fraud, embezzlement, misuse of funds, tax evasion and abusive tax avoidance. Clearly defined organized crime groups that usually have a known name, defined leadership, territorial control and identifiable membership. Loose networks of criminal associates engaging in criminal activities who fail to meet the defining characteristics of mafia-style groups. Includes foreign nationals and diaspora groups. The State's role in responding to organized crime and its effectiveness. The degree to which states have put oversight mechanisms in place to ensure against state collusion in illicit activities. A country's supranational structures and processes of interaction, policy making and concrete implementation to respond to organized crime. The degree to which states are able to control their physical and cyber territory and infrastructure against organized criminal activities. Assistance provided to victims of various forms of organized crime, including initiatives such as witness protection programs. Refers to the existence of strategies, measures, resource allocation, programmes and processes that are aimed to inhibit organized crime. Victims of human trafficking are primarily subjected to sexual exploitation and forced labour. Foreign nationals who come to the country in pursuit of work are increasingly subjected to domestic labour trafficking in rural Hungary. Meanwhile, Hungarian nationals are trafficked for forced labour within the country and outside it in the UK, Belgium and the Netherlands. Hungarian women lured into sham marriages with third-country nationals in Europe are also reportedly subjected to forced prostitution, while men are subjected to labour trafficking in agriculture, construction and factories in Western Europe. Hungarian Roma women are often manipulated by perpetrators into sex trafficking, while child sex trafficking victims generally come from state-provided childcare institutions and correctional facilities. The criminal market is mainly run by transnational organized crime groups, criminals and repeating criminal offenders. The human smuggling market in Hungary is growing and has been exacerbated by the effects of the war in Ukraine. Most human smuggling in Hungary takes place along the Hungarian—Serbian border, which has become a point of tension amid the European migrant crisis. Hungary is a transit and source country for human smuggling, especially by land, and irregular border crossings are reportedly increasing at the Hungarian—Slovakian border. Irregular migrants, often from Syria, Iraq, Pakistan and Afghanistan, are known to regularly enter Hungary by sea, usually in fishing boats, in the Danube Delta region, through Turkey to Romania. Criminal gangs from Bulgaria are known to recruit Ukrainian and Georgian nationals to carry out such smuggling activities. In addition, Serbian, Turkish and Hungarian smugglers are also involved in this criminal market. Extortion and racketeering are not common practices in Hungary. However, small-scale extortion occurs in the private sector, but is prevented in the public sector, which is heavily controlled by the state. Private-sector extortion and racketeering are connected to local gangs and criminal groups, who usually work on their own and extort from local businesses, such as restaurants and bars. Racketeering is conducted in specific markets, such as construction and small-scale sales. Hungary has seen a decrease in the number of registered criminal offences involving firearms and ammunition. However, it remains a source country for illicit firearms destined for countries such as Romania. In addition, blank-firing weapons are acquired without a licence in Hungary to be trafficked to other European countries. Small weapons manufacturers have been accused of selling illegal firearms, mainly stockpiles of old military weapons after the fall of the Soviet Union. Criminals involved in other forms of trafficking and far-right groups are known to also be involved in arms trafficking in Hungary. The war in Ukraine is expected to have consequences on the arms trafficking market in Hungary in the coming years. The market for the trade of counterfeit goods in Hungary is not large. This is mostly due to the heavy regulation of the legal market. However, there is a considerable market for counterfeit products transited through the Western Balkans and Eastern Europe. The most common counterfeit goods in the country, which are also considered dangerous to public health, are perfumes, cosmetics, clothing, toys, car parts and pharmaceutical products. Hungary is predominantly a source country for the alcoholic drinks illegally produced and smuggled inside the EU. Hungary is also a transit and destination country for the cheaper tobacco products smuggled from the Western Balkans and Belarus. Recent cases have shown that increasing quantities of tobacco from domestic production are also being illegally traded in the local market. This trend can be seen in the patterns of offences already detected and is also reflected in the declining volume of legal sales recorded by registered domestic tobacco producers. There has been an increase in flora crimes in Hungary. Illegal logging in the country has been linked to loose organized crime networks. Since the war in Ukraine, illegal logging committed by local communities for firewood has also increased, due to high energy prices. Protected plants such as snowdrops and Carpathian saffron enter or transit the country predominantly by road for subsequent sale on the black market. Even though Hungary is considered a source, destination and transit country for fauna crime, the market is not extensive and poaching has shown a decreasing trend in recent years. However, smuggling of endangered species for medicinal and decorative use, bird and avian by-products, mammal and reptile by-products, and coral derivatives are still common forms of fauna crime in the country. Furthermore, Italian hunters, assisted by their Hungarian counterparts, are reported to shoot protected birds in great quantities, to smuggle them into Italy. The high level of corruption and the developed shadow economy facilitate the activities of crime groups involved in fauna crimes in Hungary. Some of them are also involved in illegal, unreported and unregulated fishing activities in the country. The country has seen a recent spike in petrol prices due to raised fuel taxes, which resulted in an increase in petrol smuggling by illegal entrepreneurs. There are reports of a criminal group purchasing low-grade fuel oil in Poland and selling it at marked-up prices in Hungary, avoiding VAT, while using foreign companies as a front. Cases of gold laundering have also been reported. Hungary has traditionally been a transit country for heroin, originating in Afghanistan and trafficked via the Balkan route to Western Europe. However, the heroin market in Hungary is not consolidated. Turkish organized crime groups continue to be the main importers and facilitators of heroin distribution in the country, often utilizing a northern branch of the Balkan route from Bulgaria and Romania to Hungary, Austria, the Czech Republic, Poland or Germany for transportation. Cocaine is mainly transported by road from Spain or the Netherlands or is directly imported by air from South America. However, in tandem with the increase in general online shopping that occurred during the COVID pandemic, the illicit cocaine market is also flourishing online. Cannabis is the most used illicit substance among young adults aged between 18 and 34 in Hungary. Cannabis is increasingly trafficked into Hungary by Vietnamese organized crime groups based in the Czech Republic, the Western Balkans and the Netherlands. Moreover, substantial amounts of cannabis have also been intercepted entering Hungary through its shared border with Serbia. Though Hungary is primarily a destination country for cannabis, reports indicate that cannabis is cultivated on a small scale. In recent years, new psychoactive substances compete with established drugs and continue to be a source of concern. Furthermore, the use of synthetic drugs has spread among the youth in the poorest parts of the country, particularly since designer drugs like synthetic cannabinoid and cathinone are reportedly cheaper than alcohol. Cyber-dependent crime is a growing criminal market in Hungary. The frequency of data breaches has quadrupled in a few years, with malicious software infection and ransomware attacks being the most common forms of cybercrime. However, there is no indication that major criminal groups are involved in the market. Instead, it is mostly individual hackers or small hacker groups targeting private persons who are active in this criminal market. In Hungary, the financial crimes market is frequently connected to the embezzlement and misuse of funds, including both public and corporate funds. These acts primarily involve individuals and small groups, who are not part of the larger organized crime groups. Corruption based on personal connections between business owners and high-ranking public officials and politicians appears to facilitate the illegal financial crimes market. In recent years, allegations have been made of corrupt activities in governmental procurement contracts and tender processes. As Hungary is a transit country for various criminal markets, foreign criminal organizations operate in the country to varying degrees. For instance, Italian, Albanian and Georgian mafia-style groups are presently active in Hungary and engage in money laundering and cannabis trafficking. Criminal actors from the Turkish diaspora influence the heroin market, while both Slovakian and Bulgarian actors influence the human smuggling market. Domestic loose criminal networks are pervasive in almost all criminal markets present in Hungary, primarily in human trafficking and human smuggling, but also drug trafficking and petty theft. These networks are known to be involved in flora and fauna crimes as well, alongside opportunistic perpetrators. Through informal patron—client networks, members of the Hungarian economic elite influences not only major political institutions, but also controls lower-level institutions, such as local government and civil society groups. Corruption is an ongoing problem and new legislation limiting the definition of public funds could result in further challenges, as many of the companies in Hungary with close government links are supported by public funds. Furthermore, high-level politicians are connected to the oligarchs and use this connection to obtain control over certain markets, like the media. Connections between the government and private-sector actors are traditionally strong, and the government has a stronghold over private businesses. This is reflected in the preferential treatment some businesses receive from the government and the flouting of taxation and customs duty regulations. There is no evidence to suggest domestic mafia-style groups exist in Hungary. The state of governance and political leadership in Hungary is generally associated with the growth of illiberal populism. Political leaders use migration as a key campaign issue, drawing parallels between migration, crime and human smuggling in ways that critics claim stoke xenophobia and racism. In addition, independent journalists, lawyers, politicians and businesspeople in Hungary have allegedly been targeted by secret surveillance in recent years using spyware. Corruption in the political system is rampant, with several political leaders being accused of corrupt practices. The recently re-elected Prime Minister and his political party have been considered responsible of putting in place various measures that have decreased transparency and accountability. The public procurement sector is also prone to a high risk of corruption and manipulation, with companies indicating that irregular payments and bribes were commonplace in the awarding of government contracts and licences. In addition, government prosecution services have ignored or refused to investigate cases of state corruption. Hungary has ratified all relevant international treaties and conventions on organized crime and cooperates in joint investigations with Dutch, Belgian, Swiss and British authorities, and has worked with non-EU countries in training and capacity building. In , Hungary took part in the largest international law enforcement operation to date working to prevent the use of encrypted information in organized crime networks, which resulted in the confiscation of drugs, cash and cryptocurrency in Hungary. The country has various laws and policies in place to address organized crime, including drug trafficking and flora and fauna crimes, among others. Sex and labour trafficking is criminalized under law, but its legal definition is inconsistent with international law. Recent reforms have been made in the criminal code to combat human trafficking and money laundering more effectively. However, the implementation of both national and international legislation on organized crime matters is still lacking. The Hungarian judicial system is at a moderate risk for corruption, as bribes and irregular payments in return for favourable judgments sometimes occur. The current government has significantly weakened the judiciary and the Constitutional Court, and the politically influenced appointment of new Constitutional Court judges has raised concerns. Trust among the commercial sector in the independence of the judiciary has sharply declined. Furthermore, rulings not in line with party interests are harshly criticized by pro-government media and government officials. As for the penitentiary system, there are no reports suggesting overcrowding, subpar conditions and ill-treatment. Hungarian law enforcement has a special unit dedicated to combatting organized crime and an asset recovery office that is tasked to detect and freeze assets originating from criminal acts or assets in the possession of organized crime groups, as well as supporting investigations of financial crime-related cases. However, efforts need to be intensified in order for law enforcement officials to more effectively confront with the challenges posed by organized crime. Hungary is moderately equipped to withstand cyber-attacks. The Special Service for National Security manages cyber-security incidents and is the home of the computer security incident response team. In case of a cyber-security incident, this service has broad controlling rights, while other parties must cooperate with them. Hungary is a member of the Financial Action Task Force and has implemented various international standards and legislation to keep money-laundering and terrorist financing under control. The assistance provided by the Hungarian Financial Intelligence Unit significantly bolsters efforts to detect and disrupt money laundering threats and deprive criminals of these proceeds. Despite these efforts, Hungary is at medium risk of money laundering and terrorist financing, as law enforcement and other authorities have failed to use financial intelligence appropriately to investigate cases of money laundering. Hungary has a sizable informal economy and lacks transparency and predictability to encourage financial investments. Multinational corporations have complained of excessive red tape as well as preferential treatment and favouritism for Hungarian and government-linked firms. The government has tried to keep secret the contracts and finances of some state-owned companies, stating that the release of information would constitute a competitive disadvantage in the marketplace. Corruption in Hungary presents a significant risk to businesses, particularly in the tax administration and public procurement sectors. Companies report that unofficial payments are sometimes necessary to resolve certain administrative tasks, and public procurement is vulnerable to irregularities at the local level, because of strong informal relationships between businesses and political actors. Victim assistance services in Hungary, especially for trafficking victims remain scarce, uncoordinated and inadequate, exposing victims to the risk of re-victimization. A national crisis telephone service OKIT — a hour hotline for assisting victims of domestic violence, prostitution, child abuse and human trafficking — is operational, although the telephone line only offers services in Hungarian and English. The government has various acts and regulations in place that provide shelters as a victim support service. The government is committed to open three new shelters each year to build a nationwide network that includes trained staff, victim registration, a victim support hotline, as well as witness counselling, monetary aid and certificates indicating victim status. Furthermore, new provisions on the protection of witnesses and victims were introduced that lay out the criteria for special treatment and the protection of witnesses and victims. However, the lack of a transparent framework and resources devoted to regulating foreign-national labour recruitment have a negative influence on the effectiveness of the assistance provided for male victims of labour trafficking. A recovery-oriented approach is adopted when providing assistance to drug users, with an emphasis on enhancing the availability and quality of treatment services, with a particular focus on young people. Treatment is carried out by the healthcare system and social services with the participation of non-governmental institutions. However, multiple awareness and preventive measures are in place, along with thorough customs inspections to address organized crime relating to flora and fauna. Although government-sponsored efforts exist, including law enforcement-implemented awareness campaigns geared towards children, funding of the related national action plan has been reduced. The Hungarian government adopted a series of laws that hamper the operations of opposition groups, journalists, universities and NGOs critical of the government. Nonetheless, NGOs supported by the state assist human trafficking victims, running a hour hotline in English and Hungarian. As for the media landscape in the country, a significant cause for concern is that the media is increasingly concentrated in the hands of oligarchs allied with the government. Recently, a law was introduced that conflates homosexuality and gender-identity expression with paedophilia, while also banning discussion of sexual diversity in schools, the media and elsewhere. The criminal markets score is represented by the pyramid base size and the criminal actors score is represented by the pyramid height, on a scale ranging from 1 to The resilience score is represented by the panel height, which can be identified by the side of the panel. A series of 13 discussion papers, one for each illicit market considered during the development of the Index. We're constantly working to improve the Index. By participating in this survey, you will be providing us with insights and suggestions that will help us make the Index an even better resource. This report was funded in part by a grant from the United States Department of State. The opinions, findings and conclusions stated herein are those of the Global Initiative Against Transnational Organized Crime and do not necessarily reflect those of the United States Department of State. Capital Budapest. Income group High income. Population 9,, Geography type Landlocked. GINI Index Criminal markets 4. An assessment of the value, prevalence and non-monetary impacts of a specific crime type. Human trafficking 6. Human smuggling 6. Extortion and protection racketeering 2. Arms trafficking 4. Trade in counterfeit goods 4. Illicit trade in excisable goods 4. Flora crimes 4. Fauna crimes 4. Non-renewable resource crimes 3. Heroin trade 5. Cocaine trade 5. Cannabis trade 5. Synthetic drug trade 6. Cyber-dependent crimes 5. Financial crimes 5. Criminal actors 4. An assessment of the impact and influence of a specific criminal actor type on society. Mafia-style groups 1. Criminal networks 4. State-embedded actors 7. Foreign actors 5. Private sector actors 5. Political leadership and governance 4. Government transparency and accountability 3. International cooperation 4. National policies and laws 5. A state's legal action and structures put in place to respond to organized crime. Judicial system and detention 5. Law enforcement 5. Territorial integrity 6. Anti-money laundering 5. Economic regulatory capacity 4. Victim and witness support 4. Prevention 6. Non-state actors 4. Analysis Download full profile english. Trade Hungary has seen a decrease in the number of registered criminal offences involving firearms and ammunition. Environment There has been an increase in flora crimes in Hungary. Drugs Hungary has traditionally been a transit country for heroin, originating in Afghanistan and trafficked via the Balkan route to Western Europe. Cyber Crimes Cyber-dependent crime is a growing criminal market in Hungary. Financial Crimes In Hungary, the financial crimes market is frequently connected to the embezzlement and misuse of funds, including both public and corporate funds. Criminal Actors As Hungary is a transit country for various criminal markets, foreign criminal organizations operate in the country to varying degrees. Leadership and governance The state of governance and political leadership in Hungary is generally associated with the growth of illiberal populism. Criminal justice and security The Hungarian judicial system is at a moderate risk for corruption, as bribes and irregular payments in return for favourable judgments sometimes occur. Economic and financial environment Hungary is a member of the Financial Action Task Force and has implemented various international standards and legislation to keep money-laundering and terrorist financing under control. Civil society and social protection Victim assistance services in Hungary, especially for trafficking victims remain scarce, uncoordinated and inadequate, exposing victims to the risk of re-victimization. Read the analysis Listen the podcasts View all events. Next Skip. How to measure organized crime? Read more on globalinitiative. Give us feedback We're constantly working to improve the Index.

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How can I buy cocaine online in Miskolc

Official websites use. Share sensitive information only on official, secure websites. The use, distribution or reproduction in other forums is permitted, provided the original author s and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Optogenetically evoked local field potential LFP recorded from the medial prefrontal cortex mPFC of mice during basal conditions and following a systemic cocaine administration were analyzed. Blue light stimuli were delivered to mPFC through a fiber optic every 2 s and each trial was repeated times. As in the previous study, we used a surrogate data method to check that nonlinearity was present in the experimental LFPs and only used the last 1. Therefore, cocaine did not change the complexity of the recorded nonlinear data compared to the control case. The phase space of the reconstructed attractor is determined by the LFP time series and its temporally shifted versions by a multiple of some lag time. We also compared the change in the attractor shape between cocaine-injected and control using 1 dendrogram clustering and 2 Frechet distance. We also found that the lag times are about three times shorter for cocaine trials compared to control. As a result, although the phase space trajectories for control and cocaine may look similar, their dynamics is significantly different. Keywords: optogenetics, medial prefrontal cortex, electrophysiology, delay-embedding, non-linear dynamics. Pyramidal cells form wide interconnected network spanning layers 2—6 Bannister, They serve, among other functions, maintaining prefrontal cortex activity during working memory Sanchez-Vives and McCormick, and generate the UP states of persistent network activity Luczak et al. The pyramidal neurons receive inhibitory inputs from GABA interneurons, of which the most prominent group expresses the calcium-binding protein parvalbumin PV Takahata and Kato, ; Casanova and Trippe, ; Kana et al. GABAergic interneurons present significant density and morphological heterogeneities across different cortical areas Rodriguez et al. It has been shown that beta rhythm activity could be linked to autism, as it coordinates activity across fronto-parietal networks Schnitzler and Gross, ; Peter and Wolf, , and schizophrenia Liddle et al. Beta rhythm has also been associated with sensory gating Michael and Zoe, ; Hong et al. GABAergic neurons in beta band are thought to guide early stage development of radial columnar circuits of pyramidal and radial interneurons Rippon et al. Optogenetic techniques have recently been used for investigating basic questions regarding neural plasticity mechanisms Iurilli et al. Optogenetics was also used for investigating complex patterns of behavior, such as feeding Aponte et al. Optogenetics gave promising results in restoration of visual functions in blind animals Lagali et al. We used optogenetic tools to investigate the response of the local network in the medial prefrontal cortex mPFC of mice under brief light stimuli. This study used the same knock-in mouse model together with optogenetics and in vivo electrophysiology described in detail in Dilgen et al. The goal was to investigate the effects of acute cocaine on mPFC gamma oscillation and their relationship to more permanent cortical changes of long-term use of stimulants. We previously carried out a similar data mining study on the same animals under control conditions Oprisan et al. The present study is a continuation of Oprisan et al. Additionally, LFPs are easier to record, which could be useful for practical implementations of control mechanisms similar to deep brain stimulation or brain-computer interfaces Hatsopoulos and Donoghue, It has been shown that cognitive processes could modulate the temporal structure of the LFPs Pesaran et al. Such a temporal structure could be captured by the lag time distribution of delay-embedding method used here. Ongoing oscillatory activity could be reset by sensory inputs, such as visual Kambe et al. We measured the phase resetting induced by brief light stimuli using both the autocorrelation Oprisan, ; Oprisan et al. The phase resetting correction allowed an accurate estimate of the delay lag time and embedding dimension of LFP data Oprisan and Canavier, ; Oprisan et al. A detailed description of the procedures can be found in the first paper of this series Oprisan et al. The experimental protocol is the same as in Dilgen et al. As in the first paper of this series Oprisan et al. The transient response is dominated by the transient phase resetting in response to a brief 10 ms optical stimulation see Oprisan et al. While phase resetting at the neural network level can provide invaluable information regarding the ability of stimuli to drive the network with meaningful applications in, for example, epilepsy Osorio and Frei, ; Parastarfeizabadi and Kouzani, or Parkinson's Tass, , , here we focused on the steady state, unperturbed, activity of the network. The goals of this study were to 1 identify possible low-dimensional stable attractors of neural activity during the steady activity of the network, and 2 compare neural activity under systemic cocaine against the control data published in Oprisan et al. Without repeating all the mathematical details from Oprisan et al. The nonlinearity tests are necessary since some algorithms, e. To distinguish nonlinearity from purely stochastic time series Osborne and Provencale, ; Small et al. The surrogate data were generated by randomizing the Fourier transform phases, which is known to preserve the linear correlations within the original data while destroying any nonlinear structure Theiler et al. The rate of false rejections of the null hypothesis determines the necessary number of surrogates to be generated Jung et al. We used the time reversal asymmetry method Costa et al. As before Oprisan et al. Although our time series were long enough and recorded with a high sampling rate, we also explored additional null hypothesis testing methods used for testing very short time series Caillec and Montagner, A time series is said to be reversible if its probabilistic properties are invariant with respect to time reversal Diks et al. For example, a simple Gaussian random walk is time-reversal invariant Weiss, Practical implementations of temporal asymmetry measures use, for example, the difference between the probability density functions of the original and time-reversed series, or of their corresponding variances Zumbach, , , or temporal-based correlation measures over different temporal windows, or between the past and future data blocks of the same temporal length Zamparo et al. As in the previous study Oprisan et al. We used the Tisean software package to compute the time reversal asymmetry statistics both for the original and the surrogate data Hegger et al. Given that 1 our time series did not require a significant computational overhead by generating the surrogates, and 2 we already know the time scale of the processes we are interested in capturing, we did not consider additional nonlinearity tests, such as the horizontal visibility algorithm and the Kullback-Leibler divergence Lacasa et al. When using the rank ordered statistics for time reversal asymmetry see Oprisan et al. As a result, we concluded that the above statistical tests support the hypothesis of a nonlinear structure in our data. External perturbations, such as synaptic inputs, light, or mechanical pressure, alter the ongoing rhythm of oscillators by changing both their phases and amplitudes Oprisan and Canavier, ; Oprisan et al. Brief perturbations applied to intrinsic oscillatory activities lead only to transient changes of the rhythm, which eventually dissipate after a few cycles. Since our focus is on identifying similarities among steady state LFPs, any transient changes in the phases of LFP oscillations should be removed Oprisan, Phase resetting correction led to a significant increase in the coefficient of correlation from 0. Additionally, the root-mean-square rms error, i. Phase resetting of neural network activity from LFPs. C Without phase shifting to correct for the phase resetting, the average correlation was 0. D The root-mean-square rms error between the two trials decreases from The rms error computed between each trial and its corresponding cluster average further decreases see green solid circles in Figure 1D , suggesting a strong correlation among the clustered trials. As we noticed, phase resetting correction significantly lowered the distance among similar trials. For example, the distance threshold for breaking the trials in six clusters before correcting for phase resetting was about 80 units see Figure 2A and after phase correction was about 60 units see Figure 2B. In Figures 2C,D we plotted the average trace of each cluster from the optimized dendrogram shown in Figure 2B. There are some clear differences between the cluster traces, e. Although we only show figures for one of the six animals, the same numerical procedure was applied to all the data. Dendrogram-based grouping of similar LFPs. Six similar clusters are formed out of the trials both without A and with B trial phase shifts to account for network phase resetting. The distance threshold that generates six clusters is about 80 units without phase correction A and decreases to about 60 units B after phase correction. The corresponding average LFPs for each of the clusters of the optimized dendrogram show large C and smaller D amplitude oscillations. Membrane potential oscillations are generated by intricate feedback mechanisms that involve many different types of ionic channels Hille, Even the simplest conductance-based model requires evolution equations for four independent variables membrane potential, activation variable for both sodium and potassium and inactivation of potassium channels Hodgkin and Huxley, The number of independent variables required for a model is its dimensionality. For pyramidal cells realistically interconnected to mimic the mPFC network, we would expect an extremely large number of dimensions Schnitzler and Gross, However, when the actual model equations are not known, finding the dimensionality of a nonlinear system falls on experimental data. Nonlinear dynamics Abarbanel, ; Kantz and Schreiber, ; Schuster and Just, developed a set of tools for data mining, which include phase space embedding. In this paper series see also Oprisan et al. One of the challenges of delay-embedding is that we only record one-dimensional data time series of the membrane potential and use it to identify all the other independent variables that describe the system. The delay embedding method Packard et al. Geometrically, all the data points cluster along the diagonal direction of the embedding space leading to a one-dimensional attractor, regardless the complexity of the original data. However, the delay time cannot be arbitrarily large because then the reconstructed vectors are completely de-correlated. Geometrically, the data points will uniformly fill out the entire phase space without showing any particular structure Casdagli et al. The intuitive idea behind FNN is that high-dimensional phase space trajectories projected onto a lower dimensional embedding space will show self-crossing points. Such false crossing points could be eliminated by unfolding the attractor in the right dimensional space Kennel et al. Every 1. The lag time was estimated both with 1 the autocorrelation Casdagli et al. The autocorrelation measures the amount of linear correlation between the time series and a time-shifted version of itself. By selecting for the lag time the first zero crossing of the autocorrelation see Figure 3A , we ensure that any linear correlation between the two time series was removed Abarbanel, Since the autocorrelation method only eliminates the linear correlation between a time series and its time-shifted version, we also used the first minimum of the nonlinear autocorrelation function called Average Mutual Information AMI Fraser and Swinney, ; Kantz and Schreiber, to estimate the lag time see Figure 3B. The distribution of all autocorrelation-based lag times for animal 1 is shown in Figure 3C and the corresponding dendrogram-based cluster averages are given in Table 1. Time lag estimation. Once we obtained a consistent estimate of the lag time, the Tisean package was used for computing the embedding dimension of the data see Oprisan et al. Distance ratio Kennel et al. Too small of a distance ratio leads to an overestimation of the percentage of false neighbors, whereas too large of a distance ratio gives a large number of false positives. For example, for large distance ratios, e. Percentage of false nearest neighbors. B Spurious temporal correlations among too closely spaced data points were removed by different Theiler windows from to 8, samples, i. The percentage of FNN drops below 0. Strong temporal correlations are expected among data points that are close to each other Theiler, ; Theiler et al. As a result, such data points should be removed, i. We tested a wide range of Theiler windows from to 8, sampling times, which allowed us to account for any possible strong temporal correlation of closely spaced data points. For all Theiler windows tested, the percentage of FNN dropped below 0. Although we tested a wide range of Theiler windows, we only show five representative results in Figure 4B for two reasons: 1 the trend in the omitted data is similar and does not add anything to the data shown in Figure 4B , and 2 avoid figure cluttering. For each trial, the phase space attractor was reconstructed using its corresponding delay lag time, of which we only show two examples from each cluster, represented by the red and green thin lines in Figure 5. For each cluster, we also show the average reconstructed trace with the thick blue line in Figure 5. Although it seems as if all the attractors are different, they are topologically equivalent see Oprisan et al. Indeed, the attractor in Figure 5D could be morphed into the one shown in Figure 5F by twisting the upper half of the attractor with respect to the lower half. Reconstructed 3-dimensional attractors. For each of the six dendrogram-based clusters see Figure 2B two randomly selected trials red and green thin lines together with the cluster average blue thick line show the reconstructed attractors. The cluster average blue thick line only serves as a visual aid to guide us gauge if the two randomly selected trials from the same cluster remain close to each other al all times. The detailed procedure described above was also applied to the other five data sets from the different animals not shown. What did we learn from analyzing the neural activity under cocaine? First, we found that the delay embedding method also works for the cocaine case as well see Oprisan et al. Second, we found that the embedding dimension is still three, the same as for the control data in Oprisan et al. This means that the mathematical model that could describe both the control and the cocaine cases only require three independent variables. This is significant because it opens the possibility of deriving a single mathematical model, possibly with only slightly different control parameters to describe both control and cocaine results. Are control data truly different in a significant way when compared against cocaine to warrant such a hypothesis? To answer this question, we compared the data side-by-side from the same animals before and after cocaine using a dendrogram similarity measure. For each of the six animals, we concatenated the trials before cocaine trial index from 1 to with the trials after cocaine trial index to in a single trial file. As it was described above, after performing appropriate phase shifting to account for the transient phase resetting induced by the light stimulus see also Oprisan et al. If the neural activity patterns before and after cocaine are totally distinct, then we would expect that they separate in clusters with no overlap. A very high degree of similarity would be troubling from the modeling point of view since it would indicate that we cannot distinguish between the two conditions using this dendrogram method. For each cluster, we computed the percentage of mixing between before and after cocaine trials by using the formula:. If a dendrogram cluster contains only one category of trials either only before or only after cocaine trials , then the overlap is zero and the separation between before and after cocaine trials is maximum possible. However, if half of the trials of a cluster are from before and the other half are from after cocaine, then the overlap is maximum possible and the dendrogram cannot discriminate between those trials. We used both the six-cluster see Figure 6A and the cluster see Figure 6B dendrograms to classify the combined trials. The difference in the average percentage of trial overlap between the two cases is not significant, i. The fact that the average percentage overlap does not change with the number of clusters of the dendrogram suggests that the amount of overlap could be determined by a true similarity among the three-dimensional reconstructed dynamics both before cocaine see Oprisan et al. As a result, it may be possible to fit the same three dimensional mathematical model to the data before cocaine with one set of model parameters and the after cocaine data with the same model but with a different set of parameters. Overlap index between before and after cocaine for each of the six animals. The overlap seem to be consistent regardless the number of clusters: in six-cluster dendrogram A the mean percentage overlap is Indeed, from a dynamical point of view, we found significant differences between before and after cocaine trials. For example, the delay times for the phase space reconstructions are significantly different see Figure 7. Although for each trial the optimal delay is different, it is clear that the distributions of delay times are also significantly different between before and after cocaine see Figure 7A. We notice that, on average, all delay times are larger for before cocaine trials compared to after cocaine see Figure 7A. We fitted the distributions with lognormal functions to capture correctly the long tail of distributions and showed that the center of the delay time distributions before and after cocaine are well separated see Figure 7B. In all animals except one, the centers of lognormal delay time distributions for before cocaine trials are two to three times longer see Figure 7B than for cocaine trials. This has a significant impact on the mathematical modeling since the delay time sets the time scale of model equations. One possible approach to modeling such a difference in delay times between control and cocaine trials could be along the line of inquiry of previous experiments done by Dilgen et al. Distribution of delay times before and after cocaine. Typical delay time distributions show a clear time scale separation between conditions: after cocaine the delay times are significantly smaller than before cocaine A. The average value of the lognormal fit for the six animals show that for all animals except one, the after cocaine mean delay time is shorter two to three times shorter than for before cocaine B. The above classification method is entirely based on dendrogram's Euclidian distance between phase shifted trials. However, the one-dimensional time series do not tell the entire story of neural activity. Therefore, after we reconstructed the three-dimensional attractors using the delay-embedding method, we computed the Frechet distance between phase space reconstructed trajectories Frechet, Frechet distance can be intuitively formulated in terms of a man walking a dog on a leash. The man walks along one curve whereas the dog along the other and Frechet distance is the shortest leash that is sufficient for traversing both curves Eiter and Mannila, In other words, the Frechet distance is a measure of the similarity between two curves in any metric space by taking into account the location and ordering of the points along the curves Eiter and Mannila, We used a readily available Matlab implementation of Frechet distance algorithm Danziger, and computed all distances between any possible combinations of the trials before cocaine bc with the trials after cocaine ac for all six animals. For example, the top left square shows the color-coded Frechet distance between the trials before cocaine for the first animal labeled bc1 and the trials after cocaine for the first animal labeled ac1. Deep blue colors indicate small Frechet distances, i. We must emphasize that this is a different kind of similarity measure compared to the dendrogram similarity described above. This is because the Frechet distance was computed between the three-dimensional reconstructed attractors rather than the one-dimensional LFPs. As a result, Frechet distance includes dynamic information regarding both the lag time and the embedding dimension of the reconstructed attractors. A cursory inspection of Figure 8 suggests some patterns. For example, all after cocaine trials for animal 3 ac3 have large Frechet distances to any control trial across all animals bc1 to bc6. Similarly, it seems that the control data for animal 4 bc4 have consistent large Frechet distances with respect to all after cocaine trials across all animals ac1 to ac6. The dynamic information contained in the Frechet distance plots shown in Figure 8 could potentially provide additional hints regarding the time scales of variables involved in a future modeling of LFPs. A consistent blue color due to a small Frechet distance between trials suggests very similar phase space dynamics, i. Frechet distance between the control, before cocaine bc and after cocaine ac trials for all six animals. Each white-bordered square contains the color-coded Frechet distance between the control bc trials and the after cocaine ac trials. Deep blue colors mean small Frechet distance and suggests more similar phase space trajectories. The delay time for each trial was estimated using both the autocorrelation and the average mutual information functions see Table 1. We found topologically similar phase space attractors that could be morphed into each other through an appropriate change in delay time see Oprisan et al. Both the study on control data Oprisan et al. This overlap suggests that there may be a common, invariant, part of the mathematical model that describes both control and cocaine trials. At the same time, the significant difference in the delay times between control and cocaine trials see Figure 7 could lead to different phase space dynamics. This finding suggests that although there may be some similarities between control and cocaine trials, the differences in the delay times could be interpreted as two different time scales for the two experiments. Additionally, the Frechet distance plots shown in Figure 8 provide an intuitive and global understanding of potentially similar time scales between different trials as represented by blue colors. This study complements a previous Fourier-based analysis done by our group Dilgen et al. For the Fourier-based analysis, power spectral densities before and during the optogenetic stimulation were computed. It was found that stimulation at 40 Hz significantly increased oscillations and induced a clear peak in the gamma range see Figure 3 in Dilgen et al. The effect of cocaine in the Fourier-based analysis was reflected in a decrease in bandwidth of induced oscillations see Figure 4 in Dilgen et al. Applications of nonlinear dynamics methods to neuroscience are based on the assumption that the central nervous system is a nonlinear dynamical system exhibiting deterministic chaos. A small error in the former will produce an enormous error in the latter. Such sensitivity of complex, nonlinear, systems to small variations in initial conditions are particularly important in computational neuroscience since the evolution equations are solved using digital computers that can only represent data with a finite precision. Others related the unfolding rate of the system attractor obtained with delay-embedding to different pathological cases of epilepsy Pravitha et al. Another important clinical application of delay-embedding include the detection of cardiac arrhythmia Ravelli and Antolini, ; Richter and Schreiber, or the correlation between anxiety and electrocardiogram complexity Radhakrishna and Vikram, Other optogenetic modeling studies used a bottom-up approach in which relevant brain areas subject to optogenetic stimulation, such as the subthalamic nucleus STN —external Globus Pallidus GPe subnetwork, are modeled with conductance-based model neurons Ratnadurai-Giridharan et al. Although limited to only ten STN and ten GPe neurons, the model seems to capture patterns of synchronized oscillatory activity observed in Parkinsonian patients. Their numerical simulations show that optogenetic inhibition is more effective than electrical deep brain stimulation DBS Rosa et al. While further studies are needed, a data-driven model obtained with the delay-embedding method could provide subject-tailored clinical support for alternative optogenetic solutions to DBS. Other recent studies used a combination of delay embedding Kantz and Schreiber, ; Hegger et al. The method was applied to a different data structure than ours, i. The authors augmented the embedding space with extra dimensions represented by interactions between units' firing rates to account for neuronal cross-correlations. In their study, the dimension of the embedding space 10 6 was significantly larger than in our case. To handle the statistical analysis in such a high dimensional space, they used kernel-methods Hastie et al. PCA algorithms find directions which have minimal reconstruction error by describing as much variance of the data as possible with a relatively small number of orthogonal directions. To further aid with visual interpretation of the data, they also projected neural dynamics onto a 3-dimensional space using a Fisher discriminant analysis FDA technique Fisher, ; Mika et al. FDA maximizes the separability of classes in a dataset by constructing projection vectors that maximize the scatter between the classes, while minimizing the scatter within each class Duda et al. By augmenting the embedding space, the 3-dimensional visualizations seem to uniquely identify task-specific phases space attractors associated with different population states. In this study, we corrected for the transient change in the LFPs by computing the amount of phase resetting required to maximize the correlation among trials. For truly nonstationary recordings, new methods have been suggested that range from machine learning to a novel class-trajectory coherence algorithm that can estimate the departures from deterministic nature in multi-attracting dynamics Balaguer-Ballester et al. The method of class-trajectory coherence is particularly suitable for detecting subtile dynamical changes that are not detected by statistical moments and, therefore, when significant trends cannot be statistically proven Balaguer-Ballester et al. Our ultimate goal is to better understand the mechanisms of information processing and the role of the coherent 40 Hz oscillations. It is believed that this gamma rhythm of the brain is involved in higher cognitive function or consciousness Mashour, ; Lee et al. The rhythm supports information integration across different areas of the brain and helps binding neural processes that generate consciousness as shown both experimentally Tononi et al. Loss of consciousness has been revealed by decoherence of gamma rhythm John et al. The delay-embedding method has been previously used to investigate the change in the embedding dimension and lag times due to anesthetics Walling et al. Since the mice in our experiments were awake during both control and cocaine experiments, we did not find such a dramatic change in the attractors' structure. However, the underlying dynamics has a faster time scale for cocaine experiments, a detail that is only captured by analyzing the lag times. The permanent phase resetting induced by a light stimulus was removed using the pair correlations between recorded local field potentials. The phase-corrected trials were embedded in a three dimensional phase space using a delay embedding method. The main results are as follows: 1 The reconstructed attractors for cocaine trials are three-dimensional. Since previous experiments using EEGs for delay-embedding focused only on comparing the wakefulness vs. Similarly, we would like to devote future experimental studies to investigate the effect of cocaine dose on the phase space reconstruction. We hypothesize that increasing the cocaine dose should shorten the lag times to the point where neural activity leads to a dramatic change even in the topology of the attractors. Such a hypothesis aligns with the general consensus of a communication breakdown between different parts of the cerebral cortex as consciousness fades Massimini et al. SO contributed to the analysis and interpretation of data, and wrote the manuscript. JI and JH contributed to delay-embedding numerical simulations and reviewed the manuscript. TT and AL contributed to the design of the work, performed the experiments, and reviewed the manuscript. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. As a library, NLM provides access to scientific literature. Front Comput Neurosci. Find articles by Sorinel A Oprisan. Find articles by Julia Imperatore. Find articles by Jessica Helms. Find articles by Tamas Tompa. Find articles by Antonieta Lavin. Oprisan oprisans cofc. Received Jul 21; Accepted Jan 4; Collection date Open in a new tab. Mouse Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 1 1, 1, 2, 3, 2, 2, 2 4, 3, 2, 2, 4, 3 2, 2, 3, 1, 3, 4 1, 5, 1, 1, 1, 2, 5 4, 4, 4, 1, 4, 5, 6 5, 4, 2, 3, 1, 3, Similar articles. Add to Collections. Create a new collection. Add to an existing collection. Choose a collection Unable to load your collection due to an error Please try again. Add Cancel.

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