Neural information processing in the Drosophila motion vision pathway

Detecting the direction of image motion is an essential component of visual computation. An individual photoreceptor, however, does not explicitly represent the direction in which the image is shifting. Comparing neighboring photoreceptor signals over time is used to extract directional motion information from the photoreceptor array in the circuit downstream. To implement direction selectivity, two opposing models have been proposed. In both models, one input line is asymmetrically delayed compared to the other, followed by a non-linear interaction between the two input lines. The Hassenstein-Reichardt (HR) model proposes an enhancement in the preferred direction (PD): the preferred side signal is delayed and then amplified by multiplying it with the other input signal. In contrast, the Barlow-Levick (BL) detector proposes a null direction (ND) suppression, whereby the null side signal is delayed and the other input is divided by it. The motion information is computed in parallel ON and OFF pathways. T4 and T5 are the first direction-selective neurons found in the ON and in the OFF pathway, respectively. Four subtypes of T4 and T5 cells exist each responding selectively to one of the four cardinal directions: front-to-back, back-to-front, upwards, and downwards, respectively. In the first manuscript, we found that both preferred direction enhancement and null direction suppression are implemented in the dendrites of all four subtypes of both T4 and T5 cells to compute the direction of motion. We, therefore, propose a hybrid model combining both PD enhancement on the preferred side and ND suppression on the null side. This combined strategy ensures a high degree of direction selectivity already at the first stage of calculating motion direction. Further processing, in addition to synaptic mechanisms on the dendrites of T4 cells, can improve the direction selectivity of the T4 cells' output signals. Such processing might involve: 1.) transformation from voltage to calcium, and 2.) from calcium to neurotransmitter release. In the second manuscript, we used in vivo two-photon imaging of genetically encoded voltage and calcium indicators, Arclight and GCaMP6f respectively, to measure responses in Drosophila direction-selective T4 neurons. Comparison between Arclight and GCaMP6f signals revealed calcium signals to have a significantly higher direction selectivity compared to voltage signals. Using these recordings we built a model which transforms T4 voltage responses into calcium responses. The model reproduced experimentally measured calcium responses across different visual stimuli using various temporal filtering steps and a stationary non-linearity. These findings provided a mechanistic underpinning of the voltage-to-calcium transformation and showed how this processing step, in addition to synaptic mechanisms on the dendrites of T4 cells, enhances direction selectivity in the output signal of T4 neurons. The two manuscripts included in this thesis are presented chronologically and were published in peer-reviewed journals

Tradeoffs between Anonymity and Quality of Services in Data Networking and Signaling Games

Timing analysis has long been used to compromise users\u27 anonymity in networks. Even when data is encrypted, an adversary can track flows from sources to the corresponding destinations by merely using the correlation between the inter-packet timing on incoming and outgoing streams at intermediate routers. Anonymous network systems, where users communicate without revealing their identities, rely on the idea of Chaum mixing to hide `networking information\u27. Chaum mixes are routers or proxy servers that randomly reorder the outgoing packets to prevent an eavesdropper from tracking the flow of packets. The effectiveness of such mixing strategies is, however, diminished under constraints on network Quality of Services (QoS)s such as memory, bandwidth, and fairness. In this work, two models for studying anonymity, packet based anonymity and flow based anonymity, are proposed to address these issues quantitatively and a trade-off between network constraints and achieved anonymity is studied. Packet based anonymity model is proposed to study the short burst traffic arrival models of users such as in web browsing. For packet based anonymity, an information theoretic investigation of mixes under memory constraint and fairness constraint is established. Specifically, for memory constrained mixes, the first single letter characterization of the maximum achievable anonymity for a mix serving two users with equal arrival rates is provided. Further, for two users with unequal arrival rates the anonymity is expressed as a solution to a series of finite recursive equations. In addition, for more than two users and arbitrary arrival rates, a lower bound on the convergence rate of anonymity is derived as buffer size increases and it is shown that under certain arrival configurations the lower bound is tight. The adverse effects of requirement of fairness in data networking on anonymous networking is also studied using the packet based anonymity model and a novel temporal fairness index is proposed to compare the tradeoff between fairness and achieved anonymity of three diverse and popular fairness paradigms: First Come First Serve, Fair Queuing and Proportional Method. It is shown that FCFS and Fair Queuing algorithms have little inherent anonymity. A significant improvement in anonymity is therefore achieved by relaxing the fairness paradigms. The analysis of the relaxed FCFS criterion, in particular, is accomplished by modeling the problem as a Markov Decision Process (MDP). The proportional method of scheduling, while avoided in networks today, is shown to significantly outperform the other fair scheduling algorithms in anonymity, and is proven to be asymptotically optimal as the buffer size of the scheduler is increased. Flow based anonymity model is proposed to study long streams traffic models of users such as in media streaming. A detection theoretic measure of anonymity is proposed to study the optimization of mixing strategies under network constraints for this flow based anonymity model. Specifically, using the detection time of the adversary as a metric, the effectiveness of mixing strategies is maximized under constraints on memory and throughput. A general game theoretic model is proposed to study the mixing strategies when an adversary is capable of capturing a fraction of incoming packets. For the proposed multistage game, existence of a Nash equilibrium is proven, and the optimal strategies for the mix and adversary were derived at the equilibrium condition.It is noted in this work that major literature on anonymity in Internet is focused on achieving anonymity using third parties like mixes or onion routers, while the contributions of users\u27 individual actions such as accessing multiple websites to hide the targeted websites, using multiple proxy servers to hide the traffic routes are overlooked. In this thesis, signaling game model is proposed to study specifically these kind of problems. Fundamentally, signaling games consist of two players: senders and receivers and each sender belongs to one of multiple types. The users who seek to achieve anonymity are modeled as the sender of a signaling game and their types are identified by their personal information that they want to hide. The eavesdroppers are modeled as the receiver of the signaling game. Senders transmit their messages to receivers. The transmission of these messages can be seen as inevitable actions that a user have to take in his/her daily life, like the newspapers he/she subscribes on the Internet, online shopping that he/she does, but these messages are susceptible to reveal the user identity such as his/her political affiliation or his/her affluence level. The receiver (eavesdropper) uses these messages to interpret the senders\u27 type and take optimal actions according to his belief of senders\u27 type. Senders choose their messages to increase their reward given that they know the optimal policies of the receivers for choosing the action based on the transmitted message. However, sending the messages that increases senders\u27 reward may reveal their type to receivers thus violating their privacy and can be used by eavesdropper in future to harm the senders. In this work, the payoff of a signalling game is adjusted to incorporate the information revealed to an eavesdropper such that this information leakage is minimized from the users\u27 perspective. The existence of Bayesian-Nash equilibrium is proven in this work for the signaling games even after the incorporation of users\u27 anonymity. It is also proven that the equilibrium point is unique if the desired anonymity is below a certain threshold

Inchoate Crimes

The Indian Penal Code punishes a person for criminal intimidation that “The thought of a man is not triable for the devil himself not the thought of a man.” But when this intent is expressed in words and can be inferred from his conduct, the person can be held criminally liable. It means the law only takes notice of an intention followed by some overt act.3, which is a mere expression of one’s intention to inflict punishment, loss or pain to another. Sometimes it amount to completed offence.4The third stage is the ‘stage of attempt.’ An attempt is an overt act towards the commission of an offence after the preparation is made. For example, if a man after having procured a loaded gun pursues his enemy, but fails to overtake him or is arrested before he is able to complete the offence or fires without effect; in all these cases the man is liable for an attempt to murder. But in another situation, if a person purchases and loads a gun with the evident intention of shooting his enemy, but makes no movement to use the weapon After the stage of contemplation the next stage is known as ‘the stage of preparation.’ It consists devising or arranging the means or measures necessary for the commission of the crime. Generally the preparation to commit an offence is not punishable. The one reason behind it is the difficulty in proving it and the other is to protect the suspected person from unnecessary harassment. But there are some exceptions to this general rule. In these exceptional cases the mere preparation to commit the offences are punished because they preclude the possibility of an innocent intention