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Selling two complementary goods
No full textA seller is selling a pair of divisible complementary goods to an agent. The agent consumes the goods only in a specific ratio and freely disposes of excess in either good. The value of the bundle and the ratio are the agent’s private information. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price or a posted price mechanism for a class of distributions. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio are independently distributed
Significance of Anatomical Constraints in Virtual Try-On
No full textThe system of Virtual Try-ON (VTON) allows a user to try a product virtually. In general, a VTON system takes a clothing source and a person\u27s image to predict the try-on output of the person in the given clothing. Although existing methods perform well for simple poses, in case of bent or crossed arms posture or when there is a significant difference between the alignment of the source clothing and the pose of the target person, these methods fail by generating inaccurate clothing deformations. In the VTON methods that employ Thin Plate Spline (TPS) based clothing transformations, this mainly occurs for two reasons - (1) the second-order smoothness constraint of TPS that restricts the bending of the object plane. (2) Overlaps among different clothing parts (e.g., sleeves and torso) can not be modeled by a single TPS transformation, as it assumes the clothing as a single planar object; therefore, disregards the independence of movement of different clothing parts. To this end, we make two major contributions. Concerning the bending limitations of TPS, we propose a human AnaTomy-Aware Geometric (ATAG) transformation. Regarding the overlap issue, we propose a part-based warping approach that divides the clothing into independently warpable parts to warp them separately and later combine them. Extensive analysis shows the efficacy of this approach
Solvable model of driven matter with pinning
No full textWe present a simple model of driven matter in a 1D medium with pinning impurities, applicable to magnetic domains walls, confined colloids, and other systems. We find rich dynamics, including hysteresis, reentrance, quasiperiodicity, and two distinct routes to chaos. In contrast to other minimal models of driven matter, the model is solvable: we derive the full phase diagram for small N, and for large N, we derive expressions for order parameters and several bifurcation curves. The model is also realistic. Its collective states match those seen in the experiments of magnetic domain walls
Some Combinatorial Structures and Their Applications in Cryptography
No full textThe science of cryptography makes use of knowledge from several areas of mathematics including number theory, algebraic and combinatorial structures, probability, linear algebra, information theory and others. In this article we give a brief and selected review of some combinatorial structures and highlight their applications in some cryptograhic schemes. Among these structures are the orthogonal arrays, which were introduced by Prof C. R. Rao more than seventy years ago for applications in statistics. Their use in this new field of cryptography is yet another example of the versatility and power of these arrays
Study of restricted fractures in veins and dykes, and associated stress distribution
No full textStudying fractures in rocks is crucial for understanding the driving mechanism, stress distribution, and strength of the materials. In this present study, we aim to understand the fracturing susceptibility of long linear veins and dykes, which are often replete with fractures within them. These fractures are found to be restricted within these veins and dykes that act as rigid bodies. We consider this rigid body an inclusion embedded in an infinitely homogeneous matrix. A 2D FEM model has been used to conduct the present study, where the model results are obtained for different boundary conditions. To understand the response of the model with respect to various physical and mechanical properties, the stresses are computed and plotted against the applied conditions, which in turn represent the fracturing susceptibility. When the inclusion is placed perpendicular to the applied maximum compressive stress, the intra-inclusion stress becomes tensile, producing restricted tensile fractures. As the inclusion is rotated from this position beyond a critical angle of 28°, the intra-inclusion state of stress becomes compressive. Since the applied minimum compressive stress increases in magnitude, both tensile and shear fracture susceptibility within the inclusion decreases. Consequently, these model results are integrated to comment on the restricted fracturing in veins and dykes (competent layers) bounded by incompetent host rock (matrix)
Sublinear message bounds of authenticated implicit Byzantine agreement
No full textThis paper studies the message complexity of authenticated Byzantine agreement (BA) in synchronous, fully-connected distributed networks under an honest majority. We focus on the so-called implicit Byzantine agreement problem where each node starts with an input value and at the end a non-empty subset of the honest nodes should agree on a common input value by satisfying the BA properties (i.e., there can be undecided nodes)3. We show that a sublinear (in n, number of nodes) message complexity BA protocol under honest majority is possible in the standard PKI model when the nodes have access to an unbiased global coin and hash function. In particular, we present a randomized Byzantine agreement algorithm which, with high probability achieves implicit agreement, uses O˜(n) messages, and runs in O˜(1) rounds while tolerating (1/2−ϵ)n Byzantine nodes for any fixed ϵ\u3e0, the notation O˜ hides a O(polylogn) factor4. The algorithm requires standard cryptographic setup PKI and hash function with a static Byzantine adversary. The algorithm works in the CONGEST model and each node does not need to know the identity of its neighbors, i.e., works in the KT0 model. The message complexity (and also the time complexity) of our algorithm is optimal up to a polylog n factor, as we show a Ω(n) lower bound on the message complexity. We further extend the result to Byzantine subset agreement, where a non-empty subset of nodes should agree on a common value. Lastly, we analyze several relevant results that follow from the construction of the main result. To the best of our knowledge, this is the first sublinear message complexity result of Byzantine agreement. A quadratic message lower bound is known for any deterministic BA protocol (due to Dolev-Reischuk [JACM 1985]). The existing randomized BA protocols have at least quadratic message complexity in the honest majority setting. Our result shows the power of a global coin in achieving significant improvement over the existing results. It can be viewed as a step towards understanding the message complexity of randomized Byzantine agreement in distributed networks with PKI
Symmetric reduced-form voting
No full textWe study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probability can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti-majority. We also provide analogous results by requiring implementation by a symmetric monotone (strategy-proof) voting rule and by a symmetric unanimous voting rule. We apply our results to show that an ex ante Rawlsian rule is a convex combination of a pair of qualified majority rules
Synchronizability in randomized weighted simplicial complexes
No full textWe present a formula for determining synchronizability in large, randomized, and weighted simplicial complexes. This formula leverages eigenratios and costs to assess complete synchronizability under diverse network topologies and intensity distributions. We systematically vary coupling strengths (pairwise and three body), degree, and intensity distributions to identify the synchronizability of these simplicial complexes of the identical oscillators with natural coupling. We focus on randomized weighted connections with diffusive couplings and check synchronizability for different cases. For all these scenarios, eigenratios and costs reliably gauge synchronizability, eliminating the need for explicit connectivity matrices and eigenvalue calculations. This efficient approach offers a general formula for manipulating synchronizability in diffusively coupled identical systems with higher-order interactions simply by manipulating degrees, weights, and coupling strengths. We validate our findings with simplicial complexes of Rössler oscillators and confirm that the results are independent of the number of oscillators, connectivity components, and distributions of degrees and intensities. Finally, we validate the theory by considering a real-world connection topology using chaotic Rössler oscillators
Vermitechnology transforms hazardous red mud into benign organic input for agriculture: Insights on earthworm-microbe interaction, metal removal, and soil-crop improvement
No full textBioremediation of hazardous bauxite residues, red mud (RM), through vermicomposting has yet to be attempted. Therefore, the valorization potential of Eisenia fetida in various RM and cow dung (CD) mixtures was compared to aerobic composting. Earthworm fecundity and biomass growth were hindered in RM + CD (1:1) feedstock but enhanced in RM + CD (1:3). The pH of highly alkaline RM-feedstocks sharply reduced (\u3e17%) due to vermicomposting. N, P, and K availability increased dramatically with Ca and Na reduction under vermicomposting. Additionally, ∼40–60% bioavailable metal fractions were transformed to obstinate (organic matter and residual bound) forms upon vermicomposting. Consequently, the total metal concentrations were significantly reduced with considerably high earthworm bioaccumulation. Microbial growth and enzyme activity were more significant under vermicomposting than composting. Correlation statistics revealed that microbial augmentation significantly facilitated a metal reduction in RM-vermibeds. Eventually, RM-vermicompost stimulated sesame growth and improved soil health with the least heavy metal contamination to soil and crop
ADHDNet: A DNN Based Framework for Efficient ADHD Detection from fMRI Dataset
No full textThe study of functional connectivity is an evolving field of research in brain network-based analysis of neurological disorders. The interconnection between various brain regions is affected due to different neuro-disorders. Attention Deficit Hyperactivity Disorder (ADHD) has been studied using complex network-based features from the ADHD-200 competition fMRI dataset. The objective is to classify a typically developing subject from one showing a mature stage of acute symptoms (e.g., insufficient attention and/or hyperactivity). ADHD symptoms, being difficult to diagnose efficiently, will, if successfully detected computationally, lead to suitable clinical intervention and improved outcomes. The paper’s novelty is to capture the change of functional connectivity between brain regions of interest (ROIs) due to the ADHD syndrome using the brain atlas (MSDL, BASC-64/444) and complex network measures. A novel 5-layered Deep Neural Network (ADHDNet) has been implemented in this paper for efficient computer-aided diagnosis of ADHD. The output is compared with the traditional and best-performing machine learning technique Gradient Boosting as the dataset used is imbalanced between control population and mature-ADHD patients. SMOTE, Random Under (RUS), and Over (ROS) Samplers have been employed to deal with the data imbalance. This study is unique in its focus on the efficient detection of ADHD cases using complex network concepts as the feature extractor. The best performing results are 100% and 93% test-accuracies from BASC-64 + RUS and MSDL + ROS, respectively. The proposed ADHDNet provides consistently excellent and stable results based on evaluation metrics such as F1-score, accuracy, and Area under the ROC Curve(AUC)