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    Some Theorems on Minimum Variance Estimation

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    Sperm intrusion into the implantation-stage blastocyst and its potential biological significance

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    The human embryo derives from fusion of oocyte and sperm, undergoes growth and differentiation, resulting in a blastocyst. To initiate implantation, the blastocyst hatches from the zona pellucida, allowing access from external inputs. Modelling of uterine sperm distribution indicates that 200-5000 sperm cells may reach the implantation-stage blastocyst following natural coitus. We show ultrastructural evidence of sperm cells intruding into trophectoderm cells of zona-free blastocysts obtained from the uterus of rhesus monkeys. Interaction between additional sperm and zona-free blastocyst could be an evolutionary feature yielding adaptive processes influencing the developmental fate of embryos. This process bears potential implications in pregnancy success, sperm competition and human health

    Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics

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    Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and competitive) commonly observed in systems such as the human brain and social networks. This work addresses this gap by incorporating these factors into a model that explores their impact on collective properties such as synchronization. Through simplified network representations, we investigate how the simultaneous presence of cooperative and competitive adaptations influences phase transitions. Our findings reveal a transition from first-order to second-order synchronization as the strength of higher-order interactions increases under competitive adaptation. We also demonstrate the possibility of synchronization even without pairwise interactions, provided there is strong enough higher-order coupling. When only competitive adaptations are present, the system exhibits second-order-like phase transitions and clustering. Conversely, with a combination of cooperative and competitive adaptations, the system undergoes a first-order-like phase transition, characterized by a sharp transition to the synchronized state without reverting to an incoherent state during backward transitions. The specific nature of these second-order-like transitions varies depending on the coupling strengths and mean degrees. With our model, we can control not only when the system synchronizes but also the way the system goes to synchronization

    The COLM Authenticated Encryption Scheme

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    In this work we present the COLM authenticated encryption (AE) scheme which is the second of the two winners in the defense in depth category of the CAESAR competition. COLM realizes a nonce-based authenticated encryption with associated data and uses the popular AES blockcipher as its underlying primitive. We propose two possible blockcipher instantiations (with key of length 128 or 256 bits). We also define two COLM modes of operation variants: a primary COLM0 mode for general purpose applications, and a COLMτ variant with intermediate tag generation/verification geared to support low-end devices and applications where frequent verification is required. COLM is designed with security, simplicity, and efficiency in mind. The main design goal of COLM is high security: a primary feature of the defense in depth CAESAR category. COLM provides security beyond the traditional AE security. First, COLM is secure against nonce misuse, namely, it enables security in adversarial settings where the nonce inputs to the AE scheme repeat. In contrast to standardized and popular AE algorithms, such as GCM and OCB1-3 modes, whose AE security trivially breaks down when the nonce is repeated, COLM ensures both confidentiality and authenticity (AE) security with repeated nonces. Second, our COLMτ variant enables increased security levels in situations where release of unverified ciphertext (RUP) occurs due to its ability to limit a potential leakage by frequent verifications. In this work we prove COLM secure with respect to both confidentiality and authenticity (AE) security under nonce misuse in the well-known provable security framework. Our proofs show that COLM maintains n/2-bit security levels for block sizes of n bits. Furthermore, due to the inherent parallelism on both mode and primitive levels, our software performance results show that the price paid for enhanced security does come at the cost of minimal efficiency losses. More concretely, we implement GCM, COLM, and Deoxys-II on the Kaby Lake and Coffee lake Intel platforms. Compared to the other winner in the defense in depth category Deoxys-II, our AE design COLM0 performs 10–20% faster for the 128-bit key version. Regarding the 256-bit key versions COLM0 is around 5% faster for short and 2% slower than Deoxys-II for the longer messages

    The on-line transfer rule for queueing with arrivals

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    We consider the queueing problem with arrivals, or the arrival queueing problem, where agents arrive at different (time) slots to process their jobs in a service facility and each job requires the same amount of processing time which is normalized to one. Each agent has one job to process and the facility can process only one job at each slot. We introduce a rule for the arrival queueing problem, which we call the on-line transfer rule, by adapting the minimal transfer rule of the static queueing problem (Maniquet, 2003) but incorporating the time span which each agent observes. We provide axiomatic characterizations of the on-line transfer rule by imposing the axioms of efficiency, Pareto indifference, equal treatment of equals, independence of larger costs, and consistency from later-arrived-later-served agents. We also introduce and characterize an alternative rule for the arrival queueing problem which adapts the maximal transfer rule of the static queueing problem (Chun, 2006a)

    Thermoelectric Phenomena in a Magnetic Heterostructure with AAH Modulation: Charge and Spin Figure of Merits

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    We put forward a prescription of getting a higher value of the spin-dependent figure of merit in comparison with its charge counterpart in the case of a 1D magnetic heterostructure (a ferromagnetic (FM) chain sandwiched between two non-magnetic 1D lattices) where all the site energies of the heterostructure follow cosine form of modulation defined in Aubry-Andre-Harper (AAH) model. It is shown that due to having a greater number of non-uniform peaks in its transmission spectra, the thermoelectric efficiency of this heterostructure becomes superior compared to that is obtained in a fully ferromagnetic 1D chain. It is also reported that the maximum value of the thermoelectric figure of merit (for both spin and charge-dependent cases) of the heterostructure in a specified energy range gets enhanced in a continuous manner as the disorder strength of the AAH modulation is increased. The Hamiltonian of the proposed quantum system is described within a tight-binding (TB) framework and after the evaluation of transmission probability by utilizing the non-equilibrium Green’s function (NEGF) technique, all the important thermoelectric quantities are determined on the basis of Landauer formalism. We believe that our study on this particular topic of spin caloritronics, a subject associated with temperature-dependent spin transmission through a quantum channel, may help to explore several fascinating ideas about spin-related thermoelectric efficiency in many other ferromagnetic quasicrystals

    Universal and Language-Specific Connected Speech Characteristics of Bilingual Speakers With Alzheimer’s Disease: Insights From Case Studies of Structurally Distinct Languages

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    Purpose: Connected speech analysis has been effectively utilized for the diag-nosis and disease monitoring of individuals with Alzheimer’s disease (AD). Exist-ing research has been conducted mostly in monolingual English speakers with a noticeable lack of evidence from bilinguals and non-English speakers, particu-larly in non-European languages. Using a case study approach, we character-ized connected speech profiles of two Bengali–English bilingual speakers with AD to determine the universal features of language impairments in both lan-guages, identify language-specific differences between the languages, and explore language impairment characteristics of the participants with AD in rela-tion to their bilingual language experience. Method: Participants included two Bengali–English bilingual speakers with AD and a group of age-, gender-, education-, and language-matched neurologically healthy controls. Connected speech samples were collected in first language (L1; Bengali) and second language (L2; English) using a novel storytelling task (i.e., Frog, Where Are You?). These samples were analyzed using an augmented quantitative production analysis and correct information unit analyses for pro-ductivity, fluency, syntactic and morphosyntactic features, and lexical and semantic characteristics. Results: Irrespective of the language, AD impacted speech productivity (speech rate and fluency) and semantic characteristics in both languages. Unique language-specific differences were noted on syntactic measures (reduced sen-tence length in Bengali), lexical distribution (fewer pronouns and absence of reduplication in Bengali), and inflectional properties (no difficulties with noun or verb inflections in Bengali). Among the two participants with AD, the individual who showed lower proficiency and usage in L2 (English) demonstrated reduced syntactic complexity and morphosyntactic richness in English. Conclusions: Evidence from these case studies suggests that language impairment features in AD are not universal across languages, particularly in comparison to impairments typically associated with language breakdowns in English. This study underscores the importance of establishing connected speech profiles in AD for non–English-speaking populations, especially for structurally different languages. This would in turn lead to the development of language-specific markers that can facilitate early detection of language deterioration and aid in improving diagnosis of AD in individuals belonging to underserved linguistically diverse populations

    Use of Additional Information for Current Status Data with Two Competing Risks and Missing Failure Types

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    In practice, the failure type for some subjects may be missing or uncertain in competing risks data. Analysis of such uncertain failure type in current status data with two competing risks suffers from issues of model identifiability and requires some model assumptions to deal with that (Koley and Dewanji. Journal of Applied Statistics 49(7), (2022)). In this work, we attempt to alleviate this identifiability problem using some additional information and without any such model assumption. In particular, we consider additional information in the form of some prior knowledge on the missing probabilities. Next, we briefly discuss another type of additional information from a validation sample which ascertains failure type. We consider parametric estimation of the model parameters and non-parametric estimation of the sub-distribution functions. We investigate the associated large sample properties theoretically and the finite sample properties through simulation. We also consider analysis of a real data set for the purpose of illustration

    Weak markov flows and extreme points of convex sets

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    This is a brief survey of papers of K R Parthasarathy on weak Markov flows and on extreme points of various convex sets appearing in Probability and Quantum Probability

    Weak Total Coloring Conjecture and Hadwiger’s Conjecture on Total Graphs

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    The total graph of a graph G, denoted by T (G), is defined on the vertex set V (G) ∪ E(G) with c1, c2 ∈ V (G) ∪ E(G) adjacent whenever c1 and c2 are adjacent to (or incident on) each other in G. The total chromatic number χ′′ (G) of a graph G is defined to be the chromatic number of its total graph. The well-known Total Coloring Conjecture or TCC states that for every simple finite graph G having maximum degree ∆(G), χ′′ (G) ≤ ∆(G) + 2. In this paper, we consider two ways to weaken TCC: 1. Weak TCC: This conjecture states that for a simple finite graph G, χ′′ (G) = χ(T (G)) ≤ ∆(G)+3. While weak TCC is known to be true for 4-colorable graphs, it has remained open for 5-colorable graphs. In this paper, we settle this long pending case. 2. Hadwiger’s Conjecture for total graphs: We can restate TCC as a conjecture that proposes the existence of a strong χ-bounding function for the class of total graphs in the following way: If H is the total graph of a simple finite graph, then χ(H) ≤ ω(H) + 1, where ω(H) is the clique number of H. A natural way to relax this question is to replace ω(H) by the Hadwiger number η(H), the number of vertices in the largest clique minor of H. This leads to the Hadwiger’s Conjecture (HC) for total graphs: if H is a total graph then χ(H) ≤ η(H). We prove that this is true if H is the total graph of a graph with sufficiently large connectivity. It is known that (European Journal of Combinatorics, 76, 159–174,2019) if Hadwiger’s Conjecture is proved for the squares of certain special class of split graphs, then it holds also for the general case. The class of total graphs turns out to be the squares of graphs obtained by a natural structural modification of this type of split graphs

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