On the Depth of Decision Trees with Hypotheses

In this paper, based on the results of rough set theory, test theory, and exact learning, we investigate decision trees over infinite sets of binary attributes represented as infinite binary information systems. We define the notion of a problem over an information system and study three functions of the Shannon type, which characterize the dependence in the worst case of the minimum depth of a decision tree solving a problem on the number of attributes in the problem description. The considered three functions correspond to (i) decision trees using attributes, (ii) decision trees using hypotheses (an analog of equivalence queries from exact learning), and (iii) decision trees using both attributes and hypotheses. The first function has two possible types of behavior: logarithmic and linear (this result follows from more general results published by the author earlier). The second and the third functions have three possible types of behavior: constant, logarithmic, and linear (these results were published by the author earlier without proofs that are given in the present paper). Based on the obtained results, we divided the set of all infinite binary information systems into four complexity classes. In each class, the type of behavior for each of the considered three functions does not change.

Plasmonic Nanobar-on-Mirror Antenna with Giant Local Chirality: a New Platform for Ultrafast Chiral Single-Photon Emission

Providing an additional degree of freedom for binary information encoding and nonreciprocal information transmission, chiral single photons have become a new research frontier in quantum optics. Without using complex external...

Recent Advancements in Emerging Neuromorphic Device Technologies

The explosive growth of data and information has motivated technological developments in computing systems that utilize them for efficiently discovering patterns and gaining relevant insights. Inspired by the structure and functions of biological synapses and neurons in the brain, neural network algorithms that can realize highly parallel computations have been implemented on conventional silicon transistor-based hardware. However, synapses composed of multiple transistors allow only binary information to be stored, and processing such digital states through complicated silicon neuron circuits makes low-power and low-latency computing difficult. Therefore, the attractiveness of the emerging memories and switches for synaptic and neuronal elements, respectively, in implementing neuromorphic systems, which are suitable for performing energy-efficient cognitive functions and recognition, is discussed herein. Based on a literature survey, recent progress concerning memories shows that novel strategies related to materials and device engineering to mitigate challenges are presented to primarily achieve nonvolatile analog synaptic characteristics. Attempts to emulate the role of the neuron in various ways using compact switches and volatile memories are also discussed. It is hoped that this review will help direct future interdisciplinary research on device, circuit, and architecture levels of neuromorphic systems. Corresponding author(s) Email: [email protected]

Navigator function for the conformal bootstrap

Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

Tension-free Dirac strings and steered magnetic charges in 3D artificial spin ice

Abstract3D nano-architectures presents a new paradigm in modern condensed matter physics with numerous applications in photonics, biomedicine, and spintronics. They are promising for the realization of 3D magnetic nano-networks for ultra-fast and low-energy data storage. Frustration in these systems can lead to magnetic charges or magnetic monopoles, which can function as mobile, binary information carriers. However, Dirac strings in 2D artificial spin ices bind magnetic charges, while 3D dipolar counterparts require cryogenic temperatures for their stability. Here, we present a micromagnetic study of a highly frustrated 3D artificial spin ice harboring tension-free Dirac strings with unbound magnetic charges at room temperature. We use micromagnetic simulations to demonstrate that the mobility threshold for magnetic charges is by 2 eV lower than their unbinding energy. By applying global magnetic fields, we steer magnetic charges in a given direction omitting unintended switchings. The introduced system paves the way toward 3D magnetic networks for data transport and storage.

Low-Cost Thermal Camera-Based Counting Occupancy Meter Facilitating Energy Saving in Smart Buildings

Using passive infrared sensors is a well-established technique of presence monitoring. While it can significantly reduce energy consumption, more savings can be made when utilising more modern sensor solutions coupled with machine learning algorithms. This paper proposes an improved method of presence monitoring, which can accurately derive the number of people in the area supervised with a low-cost and low-energy thermal imaging sensor. The method utilises U-Net-like convolutional neural network architecture and has a low parameter count, and therefore can be used in embedded scenarios. Instead of providing simple, binary information, it learns to estimate the occupancy density function with the person count and approximate location, allowing the system to become considerably more flexible. The tests show that the method compares favourably to the state of the art solutions, achieving significantly better results.

A New Concept of Information Based on Heisenberg's Uncertainty Principle and Its Experimental Verification

This study is the first use of Heisenberg's energy-time uncertainty principle to define information quantitatively from a measuring perspective: the smallest error in any measurement is a bit of information, i.e., 1 (bit)=(2∆E ∆t)⁄ℏ. If the input energy equals the Landauer bound, the time needed to write a bit of information is 1.75x10-14 s. Newton's cradle was used to experimentally verify the information-energy-mass equivalences deduced from the aforementioned concept. It was observed that the energy input during the creation of a bit of (binary) information is stored in the information carrier in the form of the doubled momentum or the doubled “momentum mass” (mass in motion) in both classical position-based and modern orientation-based information storage. Furthermore, the experiments verified our new definition of information in the sense that the higher the energy input is, the shorter the time needed to write a bit of information is. Our study may help understand the fundamental concept of information and the deep physics behind it.

Development of binary information compression methods based on the binomial numerical function

The application of data compression methods is an effective means of improving the performance of information systems. At the same time, interest is aroused to the methods of compression without information loss which are distinguished by their versatility, low needs of costs during implementation, and the possibility of self-control. In this regard, the application of binomial numbering systems is promising. The numerical function of the binomial numbering system is used for compression. It makes it possible to put sequences in one-to-one compliance with their numbers. In this case, the transition from binary combinations to binomial numbers is used as an intermediate stage. During the study, theorems were formulated that indicate properties of compressing and restoring the mappings as well as the ways of their implementation. Models of compression processes were obtained on the basis of a numerical function, both for the case of compressible equilibrium combinations and the case when sequences of a general form are to be compressed. The compression models include coding steps based on binary binomials. The study results show the effectiveness of applying the compression based on the binomial numerical function. A 1.02 times increase in speed of information transmission through a communication channel was observed in the worst case and 18.29 times in the best case depending on the number of ones in 128-bit equilibrium combinations. The proposed methods are advantageous due to their high compression ratio (from 1.01 to 16 times for general 128-bit sequences) and versatility: combinations are compressed in which the number of ones is 75 % of their total variation range. The developed methods ensure control of errors during conversions. They are undemanding to computation resources and feature low implementation costs.

Digital watermarking of 3D disparity map based images for transaction tracking

In this thesis, the basics of disparity map and watermarking are reviewed extensively. In order to embed binary information into images, a 3D image watermarking system was proposed. This embedded information was to survive the 3D Image rendering process of Disparity maps, to help identify malicious user who would distribute the watermarked image through an unauthorized system. The proposed system adopted the concept of hidden pixel and introduced an algorithm that identifies all known hidden pixels within the image. This information is combined with the Disparity map to generate a hidden pixel disparity map (HPDM); using the information in the HPDM a decision matrix is generated. This decision matrix is used to guide the watermark embedding process to ensure that information embedded in the Left Image can survive the 3D rendering process. Using the decision matrix, the watermark detector is capable of extracting the image from either the left or right image with no effect on the overall bit rate. This achievement is due to two original additions to the detection process: (1) Reverse rendering and (2) Cyclical Redundancy check. The proposed reverse rendering process expands the decision matrix into a reduced disparity map. This reduced disparity map is used to reverse the right image into a reduced left image. The identification of the image (left or right) is achieved through the use of a CRC check, which is also capable of detecting any errors in the extracted message, thus reducing the number of misidentification. The proposed system was implemented and tested using MATLAB. The bit efficiency of the proposed system varied between 38% and 88%. This variance is caused by the complexity of the depth scene as well as the cost function used in the depth estimation process. The watermark embedding system proposed had a PSNR of 45 dB (when no mark was embedded); this value is primarily attributed to some of the quantization that occurs during the DCT transform. However, a PSNR of 33dB is attained when the watermark was added at full strength.

Digital watermarking of 3D disparity map based images for transaction tracking

In this thesis, the basics of disparity map and watermarking are reviewed extensively. In order to embed binary information into images, a 3D image watermarking system was proposed. This embedded information was to survive the 3D Image rendering process of Disparity maps, to help identify malicious user who would distribute the watermarked image through an unauthorized system. The proposed system adopted the concept of hidden pixel and introduced an algorithm that identifies all known hidden pixels within the image. This information is combined with the Disparity map to generate a hidden pixel disparity map (HPDM); using the information in the HPDM a decision matrix is generated. This decision matrix is used to guide the watermark embedding process to ensure that information embedded in the Left Image can survive the 3D rendering process. Using the decision matrix, the watermark detector is capable of extracting the image from either the left or right image with no effect on the overall bit rate. This achievement is due to two original additions to the detection process: (1) Reverse rendering and (2) Cyclical Redundancy check. The proposed reverse rendering process expands the decision matrix into a reduced disparity map. This reduced disparity map is used to reverse the right image into a reduced left image. The identification of the image (left or right) is achieved through the use of a CRC check, which is also capable of detecting any errors in the extracted message, thus reducing the number of misidentification. The proposed system was implemented and tested using MATLAB. The bit efficiency of the proposed system varied between 38% and 88%. This variance is caused by the complexity of the depth scene as well as the cost function used in the depth estimation process. The watermark embedding system proposed had a PSNR of 45 dB (when no mark was embedded); this value is primarily attributed to some of the quantization that occurs during the DCT transform. However, a PSNR of 33dB is attained when the watermark was added at full strength.