The key to understanding vision is to acquire insight into the sensory coding of indi- vidual neurons. To this end, major advances were done over the past 50 years in fitting models to neural data to identify the mapping from sensory space to neural responses. Especially the advance of DNNs in neuroscience allowed for model fits with excellent predictive power. However, such advanced neural models are complex, and their poor in- terpretability has so far hindered deeper understanding of the principles of visual coding. To address this issue, a recent study proposed a method which identifies the stimulus that activates the neuron the most. However, the sensory coding of highly non-linear neurons, which are abundant already at the earliest stages of visual processing, is too complex for a single stimulus to sufficiently characterize it. A more robust way to char- acterize this coding is through identifying the input sub-space within which the neuron is activated identically - i.e. finding invariances of the neuron's sensory representation. In this thesis, a novel approach for finding such invariant stimuli is proposed. The proposed technique is based on a generator neural network, which maps Gaussian noise from latent space to a stimulus set which equally activates a given neuron. The method demonstrated the...

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Certain properties of optimal bitwise APP (A Posteriori Probability) decoding of binary linear block codes are studied. The focus is on the Probability Density Function (<i>pdf</i>) of the bit Log-Likelihood-Ratio (<i>LLR</i>). A general channel model with discrete (not necessarily binary) input and discrete or continuous output is considered. It is proved that under a set of mild conditions on the channel, the <i>pdf</i> of the bit <i>LLR</i> of a specific bit position is independent of the transmitted code-word. It is also shown that the <i>pdf</i> of a given bit <i>LLR</i>, when the corresponding bit takes the values of zero and one, are symmetric with respect to each other (reflection of one another with respect to the vertical axis). In the case of channels with binary inputs, a sufficient condition for two bit positions to have the same <i>pdf</i> is presented. An analytical method for approximate performance evaluation of binary linear block codes using an Additive White Gaussian Noise (AWGN) channel model with Binary Phase Shift Keying (BPSK) modulation is proposed. The pdf of the bit LLR is expressed in terms of the Gram-Charlier series expansion. This expansion requires knowledge of the statistical moments of the bit <i>LLR</i>. An analytical method for calculating these moments which is based on some recursive calculations involving certain weight enumerating functions of the code is introduced. It is proved that the approximation can be as accurate as desired, using enough numbers of terms in the Gram-Charlier series expansion. A new method for the performance evaluation of Turbo-Like Codes is presented. The method is based on estimating the <i>pdf</i> of the bit <i>LLR</i> by using an exponential model. The moment matching method is combined with the maximum entropy principle to estimate the parameters of the new model. A simple method is developed for computing the Probabilities of the Point Estimates (PPE) for the estimated parameters, as well as for the Bit Error Rate (BER). It is demonstrated that this method requires significantly fewer samples than the conventional Monte-Carlo (MC) simulation.

We investigate semiclassical contributions to correlation functions in N = 1 supersymmetric gauge theories. Our principal example is the gluino condensate, which signals the breaking of chiral symmetry, and should be exactly calculable, according to a persymmetric non-renormalisation theorem. However, the two calculational approaches previously employed, SCI and WCI methods, yield different values of the gluino condensate. We describe work undertaken to resolve this discrepancy, involving a new type of calculation in which the space is changed from R(^4) to the cylinder R(3) x S(1) This brings control over the coupling, and supersymmetry ensures that we are able to continue to large radii and extract answers relevant to R(^4). The dominant semiclassical configurations on the cylinder are all possible combinations of various types of fundamental monopoles. One specific combination is a periodic instanton, so monopoles are the analogue of the instanton partons that have been conjectured to be important at strong coupling. Other combinations provide significant contributions that are neglected in the SCI approach. Monopoles are shown to generate a superpotential that determines the quantum vacuum, where the theory is confining. The gluino condensate is calculated by summing the direct contributions from all fundamental monopoles. It is found to be in agreement with the WCI result for any classical gauge group, whereas the values for the exceptional groups have not been calculated before. The ADS superpotential, which describes the low energy dynamics of matter in a supersymmetric gauge theory, is derived using monopoles for all cases where instantons do not contribute. We report on progress made towards a two monopole calculation, in an attempt to quantify the missed contributions of the SCI method. Unfortunately, this eventually proved too complicated to be feasible.

A dissertation submitted to the University of the Witwatersrand, Faculty of Science in ful lment of the academic requirements of the degree of Master of Science. Johannesburg, 2015. / The gauge/gravity correspondence is a conjectured exact duality between quantum eld theories and theories of quantum gravity. A very simple gauge/string duality, claims an equivalence between the Gaussian matrix model and the topological A-model string theory on P1. In this dissertation we study this duality, proposing concrete operators in the matrix model that are dual to gravitational descendants of the puncture operator of the topological string theory. We test our proposal by showing that a large number of matrix model correlators are in complete agreement with correlators in the dual topological string theory. Contact term interactions, as proposed by Gopakumar and Pius, play an interesting and non-trivial role in the duality.

A research project submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment for the degree of Master of Science in Physics. May 25, 2017. / This project addresses the study of the memory effect. We review the effect in electromagnetism, which is an abelian gauge theory. We prove that we can shift the phase factor by performing a gauge transformation. The gauge group is U(1). We extend the study to the nonabelian gauge theory by computing the memory in SU(2) which vanishes up to the first order Taylor expansion. Keywords: Memory Effect, Aharonov-Bohm effect, Nonabelian Gauge Theory, Supersymmetry / GR2018

O principal objetivo deste trabalho é estudar a quantização covariante da corda bosônica e da supercorda RNS, explorando as simetrias envolvidas, ou seja, as simetrias BRST e conforme no caso da corda bosônica e as generalizações correspondentes para a corda fermiônica. Em particular, discutimos alguns aspectos perturbativos da teoria bosônica e a construção de operadores de vértice da corda fermiônica. / The main goal of this work is to study the covariant quantization of the bosonic and RNS string theories by exploiting the involved symmetries, namely, the BRST and conformal invariance for the bosonic string and the corresponding supersymmetric generalizations for the fermionic case. In particular, we discuss some perturbative aspects of the bosonic theory and the construction of vertex operators for the fermionic string.

Neste trabalho apresentamos alguns resultados da invariância conforme e da teoria de escala para sistemas finitos. Estudamos, usando tais técnicas, dois modelos estatísticos (modelos 1 e 2). Para cada modelo obtivemos a anomalia conforme e as dimensões dos operadores energia e magnetização bem como seus respectivos descendentes / In this work we show some results of conformal invariance theory and finite-size scaling. We study by using these theories two statistical mechanics models (models 1 and 2). To each model we obtained the conformal anomaly, the dimensions of energy and magnetization operators as well their respective descendents

The search for a theory of quantum gravity has persisted through the last century. Although many beautiful theories such as string theory and loop quantum gravity have been proposed, experimental evidence to support or refute these theories has been difficult to obtain. Searching for Lorentz invariance violation (LIV) is one of a limited number of experimental tests which can be used to search for evidence of quantum gravity since new physics may only be observable at energies well beyond those present in the most energetic astrophysical objects, which are far greater than the energies accessible in a terrestrial laboratory. One method of searching for LIV is to look for energy-dependent time delays in the arrival of high-energy photons from distant astrophysical sources. We search for Lorentz invariance violation (LIV) using VERITAS, an imaging atmospheric Cherenkov telescope (IACT) located in southern Arizona. Significant TeV gamma ray flaring activity was detected from the blazar Markarian 421 on the night of February 17, 2010 (MJD 55244), which presented a good opportunity to search for delays in the energetic emission. We demonstrate the performance of two different dispersion estimation algorithms and apply these algorithms to our data to search for LIV. We find that while the emission from Markarian 421 contains significant variability, a necessary condition for an LIV detection, the presence of a constant background flux severely limits our sensitivity. We expect our findings to be useful for guiding future LIV studies, especially those using IACT data. In the latter part of this work we discuss the alignment of ground-based gamma-ray telescopes and present a digital autocollimator which will be used in the alignment system of a next-generation IACT. The configuration of our autocollimator enables measurement of the angle formed between the planar surface of a distant reflector and the line of sight over a range of ±0.126° with a precision better than 5 arcsec. We present a detailed description of the instrument and its data acquisition software that was used during laboratory testing.