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Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

This paper addresses the problem of task planning for robots that must comply with operational manuals in real-world settings. Task planning under these constraints is essential for enabling autonomous robot operation in domains that require adherence to domain-specific knowledge. Current methods for generating robot goals and plans rely on common sense knowledge encoded in large language models. However, these models lack grounding of robot plans to domain-specific knowledge and are not easily transferable between multiple sites or customers with different compliance needs. In this work, we present SayComply, which enables grounding robotic task planning with operational compliance using retrieval-based language models. We design a hierarchical database of operational, environment, and robot embodiment manuals and procedures to enable efficient retrieval of the relevant context under the limited context length of the LLMs. We then design a task planner using a tree-based retrieval augmented generation (RAG) technique to generate robot tasks that follow user instructions while simultaneously complying with the domain knowledge in the database. We demonstrate the benefits of our approach through simulations and hardware experiments in real-world scenarios that require precise context retrieval across various types of context, outperforming the standard RAG method. Our approach bridges the gap in deploying robots that consistently adhere to operational protocols, offering a scalable and edge-deployable solution for ensuring compliance across varied and complex real-world environments. Project website: saycomply.github.io.

This paper explores optimal architectures for evaluating the outputs of large language models (LLMs) using LLMs themselves. We propose a novel framework that interprets LLMs as advocates within an ensemble of interacting agents, allowing them to defend their answers and reach conclusions through a judge and jury system. This approach offers a more dynamic and comprehensive evaluation process compared to traditional human-based assessments or automated metrics. We discuss the motivation behind this framework, its key components, and comparative advantages. We also present a probabilistic model to evaluate the error reduction achieved by iterative advocate systems. Finally, we outline experiments to validate the effectiveness of multi-advocate architectures and discuss future research directions.

Star-galaxy separation is a crucial step in creating target catalogues for extragalactic spectroscopic surveys. A classifier biased towards inclusivity risks including spurious stars, wasting fibre hours, while a more conservative classifier might overlook galaxies, compromising completeness and hence survey objectives. To avoid bias introduced by a training set in supervised methods, we employ an unsupervised machine learning approach. Using photometry from the Wide Area VISTA Extragalactic Survey (WAVES)-Wide catalogue comprising 9-band $u-K_s$ data, we create a feature space with colours, fluxes, and apparent size information extracted by ${\rm P{\scriptsize RO} F{\scriptsize OUND}}$. We apply the non-linear dimensionality reduction method UMAP (Uniform Manifold Approximation and Projection) combined with the classifier ${\rm{\scriptsize HDBSCAN}}$ to classify stars and galaxies. Our method is verified against a baseline colour and morphological method using a truth catalogue from Gaia, SDSS, GAMA, and DESI. We correctly identify 99.72% of galaxies within the AB magnitude limit of $Z = 21.2$, with an F1 score of $0.9971 \pm 0.0018$ across the entire ground truth sample, compared to $0.9879 \pm 0.0088$ from the baseline method. Our method's higher purity ($0.9967 \pm 0.0021$) compared to the baseline ($0.9795 \pm 0.0172$) increases efficiency, identifying 11% fewer galaxy or ambiguous sources, saving approximately 70,000 fibre hours on the 4MOST instrument. We achieve reliable classification statistics for challenging sources including quasars, compact galaxies, and low surface brightness galaxies, retrieving 95.1%, 84.6%, and 99.5% of them respectively. Angular clustering analysis validates our classifications, showing consistency with expected galaxy clustering, regardless of the baseline classification., Comment: Accepted by MNRAS; 20 pages, 14 figures

Machine learning approaches have recently emerged as powerful tools to probe structure-property relationships in crystals and molecules. Specifically, Machine learning interatomic potentials (MLIP) can accurately reproduce first-principles data at a cost similar to that of conventional interatomic potential approaches. While MLIP have been extensively tested across various classes of materials and molecules, a clear characterization of the anharmonic terms encoded in the MLIP is lacking. Here, we benchmark popular MLIP using the anharmonic vibrational Hamiltonian of ThO$_2$ in the fluorite crystal structure. This anharmonic Hamiltonian was constructed from density functional theory (DFT) using our highly accurate and efficient irreducible derivative methods, and then used to generate molecular dynamics trajectories. This data set was used to train three classes of MLIP: Gaussian Approximation Potentials, Artificial Neural Networks (ANN), and Graph Neural Networks (GNN). The results were assessed by directly comparing phonons and their interactions, as well as phonon linewidths, phonon lineshifts, and thermal conductivity. The models were also trained on a DFT molecular dynamics dataset, demonstrating good agreement up to fifth-order for the ANN and GNN. Our analysis demonstrates that MLIP have great potential for accurately characterizing anharmonicity in materials systems at a fraction of the cost of conventional first principles-based approaches.

Spatial computing is a technological advancement that facilitates the seamless integration of devices into the physical environment, resulting in a more natural and intuitive digital world user experience. Spatial computing has the potential to become a significant advancement in the field of computing. From GPS and location-based services to healthcare, spatial computing technologies have influenced and improved our interactions with the digital world. The use of spatial computing in creating interactive digital environments has become increasingly popular and effective. This is explained by its increasing significance among researchers and industrial organisations, which motivated us to conduct this review. This review provides a detailed overview of spatial computing, including its enabling technologies and its impact on various applications. Projects related to spatial computing are also discussed. In this review, we also explored the potential challenges and limitations of spatial computing. Furthermore, we discuss potential solutions and future directions. Overall, this paper aims to provide a comprehensive understanding of spatial computing, its enabling technologies, their impact on various applications, emerging challenges, and potential solutions., Comment: Submitted to peer reviewe

Autonomous vehicles (AVs) rely on the Global Positioning System (GPS) or Global Navigation Satellite Systems (GNSS) for precise (Positioning, Navigation, and Timing) PNT solutions. However, the vulnerability of GPS signals to intentional and unintended threats due to their lack of encryption and weak signal strength poses serious risks, thereby reducing the reliability of AVs. GPS spoofing is a complex and damaging attack that deceives AVs by altering GPS receivers to calculate false position and tracking information leading to misdirection. This study explores a stealthy slow drift GPS spoofing attack, replicating the victim AV's satellite reception pattern while changing pseudo ranges to deceive the AV, particularly during turns. The attack is designed to gradually deviate from the correct route, making real-time detection challenging and jeopardizing user safety. We present a system and study methodology for constructing covert spoofing attacks on AVs, investigating the correlation between original and spoofed pseudo ranges to create effective defenses. By closely following the victim vehicle and using the same satellite signals, the attacker executes the attack precisely. Changing the pseudo ranges confuses the AV, leading it to incorrect destinations while remaining oblivious to the manipulation. The gradual deviation from the actual route further conceals the attack, hindering its swift identification. The experiments showcase a robust correlation between the original and spoofed pseudo ranges, with R square values varying between 0.99 and 1. This strong correlation facilitates effective evaluation and mitigation of spoofing signals.

Given a non-increasing function $\psi\colon\mathbb{N}\to\mathbb{R}^+$ such that $s^{\frac{n+1}{n}}\psi(s)$ tends to zero as $s$ goes to infinity, we show that the set of points in $\mathbb{R}^n$ that are exactly $\psi$-approximable is non-empty, and we compute its Hausdorff dimension. For $n\geq 2$, this answers questions of Jarn\'{i}k and of Beresnevich, Dickinson, and Velani., Comment: 20 pages, 4 figures

A pair of linear codes whose intersection is of dimension $\ell$, where $\ell$ is a non-negetive integer, is called an $\ell$-intersection pair of codes. This paper focuses on studying $\ell$-intersection pairs of $\lambda_i$-constacyclic, $i=1,2,$ and conjucyclic codes. We first characterize an $\ell$-intersection pair of $\lambda_i$-constacyclic codes. A formula for $\ell$ has been established in terms of the degrees of the generator polynomials of $\lambda_i$-constacyclic codes. This allows obtaining a condition for $\ell$-linear complementary pairs (LPC) of constacyclic codes. Later, we introduce and characterize the $\ell$-intersection pair of conjucyclic codes over $\mathbb{F}_{q^2}$. The first observation in the process is that there are no non-trivial linear conjucyclic codes over finite fields. So focus on the characterization of additive conjucyclic (ACC) codes. We show that the largest $\mathbb{F}_q$-subcode of an ACC code over $\mathbb{F}_{q^2}$ is cyclic and obtain its generating polynomial. This enables us to find the size of an ACC code. Furthermore, we discuss the trace code of an ACC code and show that it is cyclic. Finally, we determine $\ell$-intersection pairs of trace codes of ACC codes over $\mathbb{F}_4$.

Conjucyclic codes are part of a family of codes that includes cyclic, constacyclic, and quasi-cyclic codes, among others. Despite their importance in quantum error correction, they have not received much attention in the literature. This paper focuses on additive conjucyclic (ACC) codes over $\mathbb{F}_4$ and investigates their properties. Specifically, we derive the duals of ACC codes using a trace inner product and obtain the trace hull and its dimension. Also, establish a necessary and sufficient condition for an additive code to have a complementary dual (ACD). Additionally, we identify a necessary condition for an additive conjucyclic complementary pair of codes over $\mathbb{F}_4$. Furthermore, we show that the trace code of an ACC code is cyclic and provide a condition for the trace code of an ACC code to be LCD. To demonstrate the practical application of our findings, we construct some good entanglement-assisted quantum error-correcting (EAQEC) codes using the trace code of ACC codes.

Computing phonons from first-principles is typically considered a solved problem, yet inadequacies in existing techniques continue to yield deficient results in systems with sensitive phonons. Here we circumvent this issue using the lone irreducible derivative (LID) and bundled irreducible derivative (BID) approaches to computing phonons via finite displacements, where the former optimizes precision via energy derivatives and the latter provides the most efficient algorithm using force derivatives. A condition number optimized (CNO) basis for BID is derived which guarantees the minimum amplification of error. Additionally, a hybrid LID-BID approach is formulated, where select irreducible derivatives computed using LID replace BID results. We illustrate our approach on two prototypical systems with sensitive phonons: the shape memory alloy AuZn and metallic lithium. Comparing our resulting phonons in the aforementioned crystals to calculations in the literature reveals nontrivial inaccuracies. Our approaches can be fully automated, making them well suited for both niche systems of interest and high throughput approaches.

We prove that for any proper metric space $X$ and a function $\psi:(0,\infty)\to(0,\infty)$ from a suitable class of approximation functions, the Hausdorff dimensions of the set $W_\psi(Q)$ of all points $\psi$-well-approximable by a well-distributed subset $Q\subset X$, and the set $E_\psi(Q)$ of points that are exactly $\psi$-approximable by $Q$, coincide. This answers in a general setting, a question of Beresnevich-Dickinson-Velani in the case of approximation of reals by rationals, and answered by Bugeaud in that case using the continued-fraction expansion of reals. Our main result applies in particular to approximation by orbits of fixed points of a wide class of discrete groups of isometries acting on the boundary of hyperbolic metric spaces., Comment: 12 pages

Recently, large, high-quality public datasets have led to the development of convolutional neural networks that can detect lymph node metastases of breast cancer at the level of expert pathologists. Many cancers, regardless of the site of origin, can metastasize to lymph nodes. However, collecting and annotating high-volume, high-quality datasets for every cancer type is challenging. In this paper we investigate how to leverage existing high-quality datasets most efficiently in multi-task settings for closely related tasks. Specifically, we will explore different training and domain adaptation strategies, including prevention of catastrophic forgetting, for colon and head-and-neck cancer metastasis detection in lymph nodes. Our results show state-of-the-art performance on both cancer metastasis detection tasks. Furthermore, we show the effectiveness of repeated adaptation of networks from one cancer type to another to obtain multi-task metastasis detection networks. Last, we show that leveraging existing high-quality datasets can significantly boost performance on new target tasks and that catastrophic forgetting can be effectively mitigated using regularization.

Image registration is the process of bringing different images into a common coordinate system - a technique widely used in various applications of computer vision, such as remote sensing, image retrieval, and, most commonly, medical imaging. Deep learning based techniques have been applied successfully to tackle various complex medical image processing problems, including medical image registration. Over the years, several image registration techniques have been proposed using deep learning. Deformable image registration techniques such as Voxelmorph have been successful in capturing finer changes and providing smoother deformations. However, Voxelmorph, as well as ICNet and FIRE, do not explicitly encode global dependencies (i.e. the overall anatomical view of the supplied image) and, therefore, cannot track large deformations. In order to tackle the aforementioned problems, this paper extends the Voxelmorph approach in three different ways. To improve the performance in case of small as well as large deformations, supervision of the model at different resolutions has been integrated using a multi-scale UNet. To support the network to learn and encode the minute structural co-relations of the given image-pairs, a self-constructing graph network (SCGNet) has been used as the latent of the multi-scale UNet - which can improve the learning process of the model and help the model to generalise better. And finally, to make the deformations inverse-consistent, cycle consistency loss has been employed. On the task of registration of brain MRIs, the proposed method achieved significant improvements over ANTs and VoxelMorph, obtaining a Dice score of 0.8013 \pm 0.0243 for intramodal and 0.6211 \pm 0.0309 for intermodal, while VoxelMorph achieved 0.7747 \pm 0.0260 and 0.6071 \pm 0.0510, respectively

Systemic bias with respect to gender, race and ethnicity, often unconscious, is prevalent in datasets involving choices among individuals. Consequently, society has found it challenging to alleviate bias and achieve diversity in a way that maintains meritocracy in such settings. We propose (a) a novel optimization approach based on optimally flipping outcome labels and training classification models simultaneously to discover changes to be made in the selection process so as to achieve diversity without significantly affecting meritocracy, and (b) a novel implementation tool employing optimal classification trees to provide insights on which attributes of individuals lead to flipping of their labels, and to help make changes in the current selection processes in a manner understandable by human decision makers. We present case studies on three real-world datasets consisting of parole, admissions to the bar and lending decisions, and demonstrate that the price of diversity is low and sometimes negative, that is we can modify our selection processes in a way that enhances diversity without affecting meritocracy significantly, and sometimes improving it.

The dynamic portfolio optimization problem in finance frequently requires learning policies that adhere to various constraints, driven by investor preferences and risk. We motivate this problem of finding an allocation policy within a sequential decision making framework and study the effects of: (a) using data collected under previously employed policies, which may be sub-optimal and constraint-violating, and (b) imposing desired constraints while computing near-optimal policies with this data. Our framework relies on solving a minimax objective, where one player evaluates policies via off-policy estimators, and the opponent uses an online learning strategy to control constraint violations. We extensively investigate various choices for off-policy estimation and their corresponding optimization sub-routines, and quantify their impact on computing constraint-aware allocation policies. Our study shows promising results for constructing such policies when back-tested on historical equities data, under various regimes of operation, dimensionality and constraints.

Face masks in general, and N95 filtering facepiece respirators (FRs) that protect against SARS-Cov-2 virion in particular, have become scarce during the ongoing COVID-19 global pandemic. This work presents practical design principles for the fabrication of electrocharged filtration layers employed in N95 FRs using commonly available materials and easily replicable methods. The input polymer is polypropylene or polystyrene, and can include discarded plastic containers of these materials, and the fabrication setup is based on the cotton candy (CC) principle. The primary parameters underlying the CC principle are translated to simple design rules that allow anyone to construct their own fabrication system from common parts, or employ a commercial cotton candy machine with minimal modifications. Finally, basic characterization results for structural and filtration properties of electrocharged fabrics made using the CC principle are detailed., Comment: 18 pages, 11 figures, 4 tables. Electronic supplementary material is available online at https://doi.org/10.6084/m9.figshare.c.5217324

Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on storage systems. In this paper, we establish a connection between LRC codes and LCD codes. We derive some conditions on the construction of cyclic LRC codes so that they are also LCD codes. A lower bound on the minimum distance of such codes is determined. Some examples have been given to explain the construction.

We validate the use of matrix factorization for the automatic identification of relevant components from atomic pair distribution function (PDF) data. We also present a newly developed software infrastructure for analyzing the PDF data arriving in streaming manner. We then apply two matrix factorization techniques, Principal Component Analysis (PCA) and Non-negative Matrix Factorization (NMF), to study simulated and experiment datasets in the context of in situ experiment.

We consider a system of homogeneous quadratic forms with congruence conditions in $n\geq 3$ variables and prove the existence of two linearly independent integral solutions of bounded height. We also show the existence of small height integral zeros of this system avoiding a given set of hyperplanes., Comment: Fixed a significant typographical error

The present work reports the effect of Ta on densification and microstructure evolution during non-isothermal and spark plasma sintering of nanocrystalline W. Nanocrystalline W-5wt.%Ta alloy powder was synthesized using mechanical alloying. The nanocrystalline powder was characterized thoroughly using X-ray diffraction line profile analysis. Furthermore, the shrinkage behavior of nanocrystalline powder was investigated during non-isothermal sintering using dilatometry. Subsequently, the alloy powder was consolidated using spark plasma sintering up to 1600 {\deg}C. The role of Ta on stabilizing the microstructure during spark plasma sintering of nanocrystalline W was investigated in detail using electron backscatter diffraction. The average grain size of spark plasma sintered W-5wt.%Ta alloy was observed as 1.73 micron., Comment: 14 pages, 3 figures

We describe a supply chain optimization model deployed in an online fashion e-commerce company in India called Myntra. Our model is simple, elegant and easy to put into service. The model utilizes historic data and predicts the quantity of Stock Keeping Units (SKUs) to hold so that the metrics "Fulfilment Index" and "Utilization Index" are optimized. We present the mathematics central to our model as well as compare the performance of our model with baseline regression based solutions.

We aim to confirm the presence of Proxima b using independent measurements obtained with the new ESPRESSO spectrograph, and refine the planetary parameters taking advantage of its improved precision. We analysed 63 spectroscopic ESPRESSO observations of Proxima taken during 2019. We obtained radial velocity measurements with a typical radial velocity photon noise of 26 cm/s. We ran a joint MCMC analysis on the time series of the radial velocity and full-width half maximum of the cross-correlation function to model the planetary and stellar signals present in the data, applying Gaussian process regression to deal with stellar activity. We confirm the presence of Proxima b independently in the ESPRESSO data. The ESPRESSO data on its own shows Proxima b at a period of 11.218 $\pm$ 0.029 days, with a minimum mass of 1.29 $\pm$ 0.13 Me. In the combined dataset we measure a period of 11.18427 $\pm$ 0.00070 days with a minimum mass of 1.173 $\pm$ 0.086 Me. We find no evidence of stellar activity as a potential cause for the 11.2 days signal. We find some evidence for the presence of a second short-period signal, at 5.15 days with a semi-amplitude of merely 40 cm/s. If caused by a planetary companion, it would correspond to a minimum mass of 0.29 $\pm$ 0.08 Me. We find that the FWHM of the CCF can be used as a proxy for the brightness changes and that its gradient with time can be used to successfully detrend the radial velocity data from part of the influence of stellar activity. The activity-induced radial velocity signal in the ESPRESSO data shows a trend in amplitude towards redder wavelengths. Velocities measured using the red end of the spectrograph are less affected by activity, suggesting that the stellar activity is spot-dominated. The data collected excludes the presence of extra companions with masses above 0.6 Me at periods shorter than 50 days., Comment: 25 pages, 26 figures

This paper studies the joint design of user grouping, scheduling (or admission control) and precoding to optimize energy efficiency (EE) for multigroup multicast scenarios in single-cell multiuser MISO downlink channels. Noticing that the existing definition of EE fails to account for group sizes, a new metric called multicast energy efficiency (MEE) is proposed. In this context, the joint design is considered for the maximization of MEE, EE, and scheduled users. Firstly, with the help of binary variables (associated with grouping and scheduling) the joint design problem is formulated as a mixed-Boolean fractional programming problem such that it facilitates the joint update of grouping, scheduling and precoding variables. Further, several novel optimization formulations are proposed to reveal the hidden difference of convex/ concave structure in the objective and associated constraints. Thereafter, we propose a convex-concave procedure framework based iterative algorithm for each optimization criteria where grouping, scheduling, and precoding variables are updated jointly in each iteration. Finally, we compare the performance of the three design criteria concerning three performance metrics namely MEE, EE, and scheduled users through Monte-Carlo simulations. These simulations establish the need for MEE and the improvement from the system optimization.

This study investigates the efficiency of some select stock markets. Using an improved wavelet estimator of long range dependence, we show evidence of long memory in the stock returns of some emerging Asian economies. However, developed markets of Europe and the United States did not exhibit long memory thereby confirming the efficiency of developed stock markets. On the other hand, emerging Asian markets are found to be less efficient as long memory is more pronounced in these markets.

We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several linear forms using Roger's second moment formula for the Siegel transform on the space of unimodular lattices., Comment: 18 pages

We prove an analogue of the Oppenheim conjecture for a system comprising an inhomogeneous quadratic form and a linear form in $3$ variables using dynamics on the space of affine lattices.

Stain variation is a phenomenon observed when distinct pathology laboratories stain tissue slides that exhibit similar but not identical color appearance. Due to this color shift between laboratories, convolutional neural networks (CNNs) trained with images from one lab often underperform on unseen images from the other lab. Several techniques have been proposed to reduce the generalization error, mainly grouped into two categories: stain color augmentation and stain color normalization. The former simulates a wide variety of realistic stain variations during training, producing stain-invariant CNNs. The latter aims to match training and test color distributions in order to reduce stain variation. For the first time, we compared some of these techniques and quantified their effect on CNN classification performance using a heterogeneous dataset of hematoxylin and eosin histopathology images from 4 organs and 9 pathology laboratories. Additionally, we propose a novel unsupervised method to perform stain color normalization using a neural network. Based on our experimental results, we provide practical guidelines on how to use stain color augmentation and stain color normalization in future computational pathology applications., Comment: Accepted in the Medical Image Analysis journal

The long-term average performance of the MISO downlink channel, with a large number of users compared to transmit antennas of the BS, depends on the interference management which necessitates the joint design problem of scheduling and precoding. Unlike the previous works which do not offer a truly joint design, this paper focuses on formulating a problem amenable for the joint update of scheduling and precoding. Novel optimization formulations are investigated to reveal the hidden difference of convex/ concave structure for three classical criteria (weighted sum rate, max-min SINR, and power minimization) and associated constraints are considered. Thereafter, we propose a convex-concave procedure framework based iterative algorithm where scheduling and precoding variables are updated jointly in each iteration. Finally, we show the superiority in performance of joint solution over the state-of-the-art designs through Monte-Carlo simulations.

In this paper, we clarify some aspects on LCD codes in the literature. We first prove that a non-free LCD code does not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD code over finite commutative Frobenius rings. We later show that a free constacyclic code over finite chain ring is LCD if and only if it is reversible, and also provide a necessary and sufficient condition for a constacyclic code to be reversible over finite chain rings. We illustrate the minimum Lee-distance of LCD codes over some finite commutative chain rings and demonstrate the results with examples. We also got some new optimal $\mathbb{Z}_4$ codes of different lengths {which are} cyclic LCD codes over $\mathbb{Z}_4$.

This paper describes the data acquisition and trigger system of the Thin Time-of-flight PET (TT-PET) scanner. The system is designed to read out in the order of 1000 pixel sensors used in the scanner and to provide a reference timing signal to each sensor in order to measure time differences of better than 30 ps. This clock distribution is measured to have a jitter of less than 4 ps at the sensors. Collected data is locally processed before being forwarded to storage. Data flow as well as control, configuration and monitoring aspects are are also addressed.

The TT-PET collaboration is developing an MRI-compatible small animal PET scanner in which the sensitive element is a monolithic silicon pixel ASIC targeting 30 ps RMS time resolution. The photon-detection technique is based on a stack of alternating layers of high-Z photon converter and 100 $\mathrm{\mu m}$ silicon sensors, to produce a scanner with 0.5 $\mathrm{\times}$ 0.5 $\mathrm{\times}$ 0.2 $\mathrm{mm^{3}}$ granularity for precise depth-of-interaction measurement. In this paper we present the results of simulation studies for the expected data rate, time-of-flight and spatial resolution, as well as the performance of image reconstruction with and without the use of timing information., Comment: arXiv admin note: text overlap with arXiv:1811.12381

The TT-PET collaboration is developing a small animal TOF-PET scanner based on monolithic silicon pixel sensors in SiGe BiCMOS technology. The demonstrator chip, a small-scale version of the final detector ASIC, consists of a 3 x 10 pixel matrix integrated with the front-end, a 50 ps binning TDC and read out logic. The chip, thinned down to 100 {\mu}m and backside metallized, was operated at a voltage of 180 V. The tests on a beam line of minimum ionizing particles show a detection efficiency greater than 99.9 % and a time resolution down to 110 ps.

In this paper, an explicit representation and enumeration for negacyclic codes of length $2^kn$ over the local non-principal ideal ring $R=\mathbb{Z}_4+u\mathbb{Z}_4$ $(u^2=0)$ is provided, where $k, n$ are any positive integers and $n$ is odd. As a corollary, all distinct negacyclic codes of length $2^k$ over $R$ are listed precisely. Moreover, a mass formula for the number of negacyclic codes of length $2^kn$ over $R$ is given and a mistake in [Cryptogr. Commun. (2017) 9: 241--272] is corrected.

The solar radiation spectrum is important for renewable energy harvesting, as well as climate and ecological systems analysis. In addition to seasonal/annual and diurnal oscillations, the signal is composed of different frequencies ($f$) that modulate each other. This results in a continuous spectrum with a power-law dependence over the entire frequency range from 1/year up to at least 1/min. Geographical location plays an important role in determining the temporal variability of solar radiation and naturally affects its spectral power-law decay, primarily due to the latitudinal dependence of daylight duration and its seasonal variation,. Employing a model to calculate the clear sky solar radiation intensity at various global locations, we show that significant spatial variability exists, particularly versus the latitude, which we quantify via the exponent of the spectral power-law. At most locations, the spectral power-law dependence of the intermediate (1/day $< f <$ 1/hour) frequencies is different from that of the high ($f > 1/$hour) frequencies. We demonstrate the origin of this power-law dependence from simple arguments, explain its geographic dependence and discuss the implications for photovoltaic power generation and solar-driven systems, and hence the impact on grid stability.

Compressed frictional granular matter cannot flow without dilation. Upon forced shearing to generate flow, the amount of dilation may depend on the initial preparation and a host of material variables. On the basis of both experiments and numerical simulations we show that as a result of training by repeated compression-decompression cycles the amount of dilation induced by shearing the system depends only on the shear rate and on the (pre-shearing) packing fraction. Relating the rheological response to structural properties allows us to derive a scaling law for the amount of dilation after $n$ cycles of compression-decompression. The resulting scaling law has a universal exponent that for trained systems is independent of the inter-granules force laws, friction parameters and strain rate. The amplitude of the scaling law is analytically computable, and it depends only on the shear rate and the asymptotic packing fraction., Comment: 8 pages, 10 figures, Published Version

Prostate cancer (PCa) is graded by pathologists by examining the architectural pattern of cancerous epithelial tissue on hematoxylin and eosin (H&E) stained slides. Given the importance of gland morphology, automatically differentiating between glandular epithelial tissue and other tissues is an important prerequisite for the development of automated methods for detecting PCa. We propose a new method, using deep learning, for automatically segmenting epithelial tissue in digitized prostatectomy slides. We employed immunohistochemistry (IHC) to render the ground truth less subjective and more precise compared to manual outlining on H&E slides, especially in areas with high-grade and poorly differentiated PCa. Our dataset consisted of 102 tissue blocks, including both low and high grade PCa. From each block a single new section was cut, stained with H&E, scanned, restained using P63 and CK8/18 to highlight the epithelial structure, and scanned again. The H&E slides were co-registered to the IHC slides. On a subset of the IHC slides we applied color deconvolution, corrected stain errors manually, and trained a U-Net to perform segmentation of epithelial structures. Whole-slide segmentation masks generated by the IHC U-Net were used to train a second U-Net on H&E. Our system makes precise cell-level segmentations and segments both intact glands as well as individual (tumor) epithelial cells. We achieved an F1-score of 0.895 on a hold-out test set and 0.827 on an external reference set from a different center. We envision this segmentation as being the first part of a fully automated prostate cancer detection and grading pipeline.

In this paper, we study the codes over the matrix ring over $\mathbb{Z}_4$, which is perhaps the first time the ring structure $M_2(\mathbb{Z}_4)$ is considered as a code alphabet. This ring is isomorphic to $\mathbb{Z}_4[w]+U\mathbb{Z}_4[w]$, where $w$ is a root of the irreducible polynomial $x^2+x+1 \in \mathbb{Z}_2[x]$ and $U\equiv$ ${11}\choose{11}$. We first discuss the structure of the ring $M_2(\mathbb{Z}_4)$ and then focus on algebraic structure of cyclic codes and self-dual cyclic codes over $M_2(\mathbb{Z}_4)$. We obtain the generators of the cyclic codes and their dual codes. Few examples are given at the end of the paper., Comment: 10 pages

We introduce a new class of adaptive policies called periodic-affine policies, that allows a decision maker to optimally manage and control large-scale newsvendor networks in the presence of uncertain demand without distributional assumptions. These policies are data-driven and model many features of the demand such as correlation, and remain robust to parameter mis-specification. We present a model that can be generalized to multi-product settings and extended to multi-period problems. This is accomplished by modeling the uncertain demand via sets. In this way, it offers a natural framework to study competing policies such as base-stock, affine, and approximative approaches with respect to their profit, sensitivity to parameters and assumptions, and computational scalability. We show that the periodic-affine policies are sustainable, i.e. time consistent, because they warrant optimality both within subperiods and over the entire planning horizon. This approach is tractable and free of distributional assumptions, and hence, suited for real-world applications. We provide efficient algorithms to obtain the optimal periodic-affine policies and demonstrate their advantages on the sales data from one of India's largest pharmacy retailers.

A generic aggregate forming system in two dimensions (2D) is studied using canonical ensemble constant temperature molecular dynamics simulation. The aggregates form due to the competition between short range attraction and long range repulsion of pair-wise interactions. Choosing the appropriate set of interaction parameters, we focus on characterising the collective dynamics in two specific morphologies, {\it viz.} compact and string-like aggregates. We focus on the temporal evolution of the mobility of an individual particle and the dynamic change in its nearest neighbourhood, measured in terms of the Debye-Waller factor ($\bar{u}_i^2$) and the non-affine parameter ($\chi$), respectively (defined in the text), and their interrelation over several lengths of observation time $\tau_w$. The distribution for both measures are found to follow the relation: $P(x;\tau_w) \sim \tau_w^{-\gamma}x$ for the measured quantity $x$. The exponent $\gamma$ is equal to $2$ and $1$ respectively, for the compact and string-like morphologies following the ideal fractal dimension of these aggregates. A functional dependence between these two observables is determined from a detailed statistical analysis of their joint and conditional distributions. The results obtained can readily be used and verified by experiments on aggregate forming systems such as globular proteins, nanoparticle self-assembly etc. Further, the insights gained from this study might be useful to understand the evolution of collective dynamics in diverse glass-forming systems.

We report a joint experimental and theoretical investigation of the probability distribution functions (pdf's) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint pdf of normal and tangential forces together, and the marginal pdf's of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. Excellent agreements with both experimental and simulational data are reported. The proposed joint pdf (which appears new to the literature) predicts giant slip events at low pressures, again in agreement with observations., Comment: 13 pages, 15 figures

We consider a robust optimization problem in an electric power system under uncertain demand and availability of renewable energy resources. Solving the deterministic alternating current optimal power flow (ACOPF) problem has been considered challenging since the 1960s due to its nonconvexity. Linear approximation of the AC power flow system sees pervasive use, but does not guarantee a physically feasible system configuration. In recent years, various convex relaxation schemes for the ACOPF problem have been investigated, and under some assumptions, a physically feasible solution can be recovered. Based on these convex relaxations, we construct a robust convex optimization problem with recourse to solve for optimal controllable injections (fossil fuel, nuclear, etc.) in electric power systems under uncertainty (renewable energy generation, demand fluctuation, etc.). We propose a cutting-plane method to solve this robust optimization problem, and we establish convergence and other desirable properties. Experimental results indicate that our robust convex relaxation of the ACOPF problem can provide a tight lower bound.

The TT-PET collaboration is developing a PET scanner for small animals with 30 ps time-of-flight resolution and sub-millimetre 3D detection granularity. The sensitive element of the scanner is a monolithic silicon pixel detector based on state-of-the-art SiGe BiCMOS technology. The first ASIC prototype for the TT-PET was produced and tested in the laboratory and with minimum ionizing particles. The electronics exhibit an equivalent noise charge below 600 e- RMS and a pulse rise time of less than 2 ns, in accordance with the simulations. The pixels with a capacitance of 0.8 pF were measured to have a detection efficiency greater than 99% and, although in the absence of the post-processing, a time resolution of approximately 200 ps.

We report a joint experimental and theoretical investigation of cyclic training of amorphous frictional granular assemblies, with special attention to memory formation and retention. Measures of dissipation and compactification are introduced, culminating with a proposed scaling law for the reducing dissipation and increasing memory. This scaling law is expected to be universal, insensitive to the details of the elastic and frictional interactions between the granules., Comment: 11 pages, 13 figures, Supplementary information included along with the main paper

We experimentally study the statistics of force-chain evolution in a vertically-tapped two-dimensional granular packing by using photoelastic disks. In this experiment, the tapped granular packing is gradually compacted. During the compaction, the isotropy of grain configurations is quantified by measuring the deviator anisotropy derived from fabric tensor, and then the evolution of force-chain structure is quantified by measuring the interparticle forces and force-chain orientational order parameter. As packing fraction increases, the interparticle force increases and finally saturates to an asymptotic value. Moreover, the grain configurations and force-chain structures become isotropically random as the tapping-induced compaction proceeds. In contrast, the total length of force chains remains unchanged. From the correlations of those parameters, we find two relations: (i) a positive correlation between the isotropy of grain configurations and the disordering of force-chain orientations, and (ii) a negative correlation between the increasing of interparticle forces and the disordering of force-chain orientations. These relations are universally held regardless of the mode of particle motions with/without convection.

A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be approximated as a linearly elastic solid. The model approximates the loss in tensile strength of the monolayer as the surfactant concentration increases through the evolution of a damage field. Initial-boundary value problems are constructed and spatially discretized with finite element approximations to the displacement and surfactant damage fields. A comparison between model-based simulations and existing experimental observations indicates a qualitative match in both the fracture patterns and temporal scaling of the fracture process. The importance of surface tension differences is quantified by means of a dimensionless parameter, revealing thresholds that separate different regimes of fracture. These findings are supported by newly performed experiments that validate the model and demonstrate the strong sensitivity of the fracture pattern to differences in surface tension., Comment: 10 pages, 11 figures, and 3 tables

Foot stiffness underlies its mechanical function, and is central to the evolution of human bipedal locomotion. The stiff and propulsive human foot has two distinct arches, the longitudinal and transverse. By contrast, the feet of non-human primates are flat and softer. Current understanding of foot stiffness is based on studies that focus solely on the longitudinal arch, and little is known about the mechanical function of the transverse arch. However, common experience suggests that transverse curvature dominates the stiffness; a drooping dollar bill stiffens significantly upon curling it along the transverse direction, not the longitudinal. We derive a normalized curvature parameter that encapsulates the geometric principle underlying the transverse curvature-induced stiffness. We show that the transverse arch accounts for almost all the difference in stiffness between human and monkey feet (vervet monkeys and pig-tailed macaques) by comparing transverse curvature-based predictions against published data on foot stiffness. Using this functional interpretation of the transverse arch, we trace the evolution of hominin feet and show that a human-like stiff foot likely predates Homo by $\sim 1.5$ million years, and appears in the $\sim 3.4$ million year old fossil from Burtele. A distinctly human-like transverse arch is also present in early members of Homo, including Homo naledi, Homo habilis, and Homo erectus. However, the $\sim 3.2$ million year old Australopithecus afarensis is estimated to have possessed a transitional foot, softer than humans and stiffer than other extant primates. A foot with human-like stiffness probably evolved around the same time as other lower limb adaptations for regular bipedality, and well before the emergence of Homo, the longitudinal arch, and other adaptations for endurance running., Comment: 22 pages, 7 figures, 4 tables

Small drops impinging angularly on thin flowing soap films frequently demonstrate the rare emergence of bulk elastic effects working in-tandem with the more common-place hydrodynamic interactions. Three collision regimes are observable: (a) drop piercing through the film, (b) it coalescing with the flow, and (c) it bouncing off the film surface. During impact, the drop deforms along with a bulk elastic deformation of the film. For impacts that are close-to-tangential, the bounce-off regime predominates. We outline a reduced order analytical framework assuming a deformable drop and a deformable three-dimensional film, and the idealization invokes a phase-based parametric study. Angular inclination of the film and the ratio of post and pre impact drop sizes entail the phase parameters. We also perform experiments with vertically descending droplets impacting against an inclined soap film, flowing under constant pressure head. Model predicted phase domain for bounce-off compares well to our experimental findings. Additionally, the experiments exhibit momentum transfer to the film in the form of shed vortex dipole, along with propagation of free surface waves. On consulting prior published work, we note that for locomotion of water-walking insects using an impulsive action, the momentum distribution to the shed vortices and waves are both significant, taking up respectively 2/3-rd and 1/3-rd of the imparted streamwise momentum. In view of the potentially similar impulse actions, this theory is applied to the bounce-off examples in our experiments, and the resultant shed vortex dipole momenta are compared to the momenta computed from particle imaging velocimetry data. The magnitudes reveal identical order ($10^{-7}$ N$\cdot$s), suggesting that the bounce-off regime can be tapped as a simple analogue for interfacial bio-locomotion relying on impulse reactions.

We experimentally study steady Marangoni-driven surfactant transport on the interface of a deep water layer. Using hydrodynamic measurements, and without using any knowledge of the surfactant physico-chemical properties, we show that sodium dodecyl sulphate and Tergitol 15-S-9 introduced in low concentrations result in a flow driven by adsorbed surfactant. At higher surfactant concentration, the flow is dominated by the dissolved surfactant. Using Camphoric acid, whose properties are {\it a priori} unknown, we demonstrate this method's efficacy by showing its spreading is adsorption dominated.