Effective Choice and Boundedness Principles in Computable Analysis

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain choice principles which are cornerstones among Weihrauch degrees and it turns out that certain core theorems in analysis can be classified naturally in this structure. In particular, we study theorems such as the Intermediate Value Theorem, the Baire Category Theorem, the Banach Inverse Mapping Theorem and others. We also explore how existing classifications of the Hahn-Banach Theorem and Weak K"onig's Lemma fit into this picture. We compare the results of our classification with existing classifications in constructive and reverse mathematics and we claim that in a certain sense our classification is finer and sheds some new light on the computational content of the respective theorems. We develop a number of separation techniques based on a new parallelization principle, on certain invariance properties of Weihrauch reducibility, on the Low Basis Theorem of Jockusch and Soare and based on the Baire Category Theorem. Finally, we present a number of metatheorems that allow to derive upper bounds for the classification of the Weihrauch degree of many theorems and we discuss the Brouwer Fixed Point Theorem as an example

DNA Sequence Evolution through Integral Value Transformations

In deciphering the DNA structures, evolutions and functions, Cellular Automata (CA) do have a significant role. DNA can be thought of as a one-dimensional multi-state CA, more precisely four states of CA namely A, T, C, and G which can be taken as numerals 0, 1, 2 and 3. Earlier, G.Ch. Sirakoulis et al reported the DNA structure, evolution and function through quaternary logic one dimensional CA and the authors have found the simulation results of DNA evolutions with the help of only four linear CA rules. The DNA sequences which are produced through the CA evolutions, however, are seen by our research team not to exist in the established databases of various genomes although the initial seed (initial global state of CA) was taken from the database. This problem motivated us to study the DNA evolutions from a more fundamental point of view. Parallel to the CA paradigm we have devised an enriched set of discrete transformations which have been named as Integral Value Transformations (IVT). Interestingly, on applying the IVT systematically, we have been able to show that each of the DNA sequences at various discrete time instances in IVT evolutions can be directly mapped to a specific DNA sequence existing in the database. This has been possible through our efforts of getting quantitative mathematical parameters of the DNA sequences involving Fractals. Thus we have at our disposal some transformational mechanism between one DNA to another

Gradient-free activation maximization for identifying effective stimuli

A fundamental question for understanding brain function is what types of stimuli drive neurons to fire. In visual neuroscience, this question has also been posted as characterizing the receptive field of a neuron. The search for effective stimuli has traditionally been based on a combination of insights from previous studies, intuition, and luck. Recently, the same question has emerged in the study of units in convolutional neural networks (ConvNets), and together with this question a family of solutions were developed that are generally referred to as "feature visualization by activation maximization." We sought to bring in tools and techniques developed for studying ConvNets to the study of biological neural networks. However, one key difference that impedes direct translation of tools is that gradients can be obtained from ConvNets using backpropagation, but such gradients are not available from the brain. To circumvent this problem, we developed a method for gradient-free activation maximization by combining a generative neural network with a genetic algorithm. We termed this method XDream (EXtending DeepDream with real-time evolution for activation maximization), and we have shown that this method can reliably create strong stimuli for neurons in the macaque visual cortex (Ponce et al., 2019). In this paper, we describe extensive experiments characterizing the XDream method by using ConvNet units as in silico models of neurons. We show that XDream is applicable across network layers, architectures, and training sets; examine design choices in the algorithm; and provide practical guides for choosing hyperparameters in the algorithm. XDream is an efficient algorithm for uncovering neuronal tuning preferences in black-box networks using a vast and diverse stimulus space.Comment: 16 pages, 8 figures, 3 table

Proteomics in the Light of Integral Value Transformations

In this paper, Proteomics have been studied in the light of Integral Value Transformations (IVTs) which was introduced by Sk. S. Hassan et al in 2010. For case study, a Human olfactory receptor OR1D2 protein sequence has been taken and then different IVTs have been used to evolve OR1D2 into some other proteomic like sequences. It has been observed that some of the generated sequences have been mapped to another olfactory receptor in Human or in some other species. Also it has been corroborated through fractal dimension that some of the fundamental protein properties have been nearly intact, even after the mapping. This study will help to comprehend the proteomic evolutionary network with the help of IVTs

Public transport values of time

OBJECTIVES The objectives of this aspect of the study are to provide recommended valuations of: • Public transport in-vehicle time (IVT) • Walk time • Wait time/headway with appropriate modifiers according to key factors such as: • Mode user type • The mode to which the value relates • Journey distance and inter urban or urban context • Journey purpose A recommended procedure for updating values of time over time is also required. Although this issue is touched upon in this paper, a more detailed analysis is the subject of a separate aspect of the study and is reported in Working Paper 566. The Accent and Hague Consulting Group study did not cover public transport. Nor is this study conducting fresh empirical research. We must therefore base our recommendations on other existing studies. Fortunately, there is a wealth of British evidence on the value of time. Section 2 provides some background to the valuations of time for public transport users and the valuation of attributes which are important aspects of public transport use. Section 3 details the additional data that has been collected to enhance our previous data sets upon which we have conducted meta-analysis (Wardman, 2001) whilst Section 4 presents tabulations of the money values of time, and the time values of walk, wait and headway, disaggregated as far as is sensible by purpose, mode and whether the journey is urban or inter-urban. Section 5 describes the principal approach that we have adopted to explain the values of time obtained from the many different studies that are available to us. Section 6 is concerned with a regression model estimated to the money values for all travellers. From this model are extracted the money values of time and the IVT equivalent values of walk time, wait time and headway for public transport users. The IVT values can be expressed as absolute values or as relative to car users’ values. The latter is useful where recommended public transport values are derived as a series of modifiers to car users’ values. As a check of the IVT values of walk, wait and headway implied by the model estimated to money values, we report in section 7 a model estimated solely to the IVT values of walk, wait and headway. Concluding remarks are provided in section 8. Recommendations and comparisons with other aspects of the study are a feature of Working Paper 567