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Neural scaling laws have become foundational for optimizing large language model (LLM) training, yet they typically assume a single dense model output. This limitation effectively overlooks "Familial models, a transformative paradigm essential for realizing ubiquitous intelligence across heterogeneous device-edge-cloud hierarchies. Transcending static architectures, familial models integrate early exits with relay-style inference to spawn G deployable sub-models from a single shared backbone. In this work, we theoretically and empirically extend the scaling law to capture this "one-run, many-models" paradigm by introducing Granularity (G) as a fundamental scaling variable alongside model size (N) and training tokens (D). To rigorously quantify this relationship, we propose a unified functional form L(N, D, G) and parameterize it using large-scale empirical runs. Specifically, we employ a rigorous IsoFLOP experimental design to strictly isolate architectural impact from computational scale. Across fixed budgets, we systematically sweep model sizes (N) and granularities (G) while dynamically adjusting tokens (D). This approach effectively decouples the marginal cost of granularity fr

DNA databases are widely used in forensic science to identify unknown offenders. When no exact match is found, familial DNA searches can help by identifying first-degree relatives using likelihood ratios. If multiple subpopulations are relevant, likelihood ratios can be computed separately based on allele frequency estimates. Various strategies exist to combine these ratios, such as averaging allele frequencies or taking the average, maximum, or minimum likelihood ratio. While some comparisons have been made in populations like those in the U.S., their effectiveness in other regions remains unclear. This study evaluates likelihood ratio-based strategies in Southeast Asian populations, specifically Thailand, Malaysia, and Singapore. Our findings align with previous research, showing that statistical power varies across strategies. Among Thai subpopulations, the minimum likelihood ratio strategy is preferred, as it maintains high power while minimizing differences between subpopulations.

Women's health in Bangladesh faces risks due to an alarming rise in cesarean section (CS) rates, exceeding 72% in hospital-based deliveries, far surpassing the WHO's recommended limit of 15%. This study, guided by the Health Belief Model (HBM) and the Theory of Planned Behavior (TPB), explored socio-cultural factors influencing childbirth mode decisions. Among 503 survey participants, 91% of CS cases occurred against initial preferences, revealing a disconnect between health beliefs and behavior. Subjective norms, particularly family influence and social expectations, emerged as more critical in shaping CS decisions than physician recommendations.

Originally enriched categories were defined over a monoidal category, but it was gradually realized that important examples can only be included when one enriches over more general structures such as bicategories and virtual double categories. We show that, as well as allowing more examples, working over virtual double categories also gives better formal properties. We study the 2-functor sending a virtual double category to the 2-category of categories enriched over it. We show that this is a parametric right 2-adjoint, and in fact is familial. We also show how a ``families construction'' for virtual double categories can be used to give a formal construction of the 2-category of categories enriched over a virtual double category.

Familial cerebral cavernous malformation (FCCM) is a hereditary disorder characterized by abnormal vascular structures within the central nervous system. The FCCM lesions are often numerous and intricate, making quantitative analysis of the lesions a labor-intensive task. Consequently, clinicians face challenges in quantitatively assessing the severity of lesions and determining whether lesions have progressed. To alleviate this problem, we propose a quantitative statistical framework for FCCM, comprising an efficient annotation module, an FCCM lesion segmentation module, and an FCCM lesion quantitative statistics module. Our framework demonstrates precise segmentation of the FCCM lesion based on efficient data annotation, achieving a Dice coefficient of 93.22\%. More importantly, we focus on quantitative statistics of lesions, which is combined with image registration to realize the quantitative comparison of lesions between different examinations of patients, and a visualization framework has been established for doctors to comprehensively compare and analyze lesions. The experimental results have demonstrated that our proposed framework not only obtains objective, accurate, and

Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, significant results of this kind are concerning. Rather than testing a single centre, this paper proposes testing a family of plausible centres, such as that induced by the Huber loss function (the Huber family). Each centre in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a novel pathwise optimization routine to fit the Huber family. The favourable properties of the new test are demonstrated theoretically and experimentally. Two examples from psychology serve as real-world case studies.

A classical result due to Diers shows that a copresheaf $F\colon\mathcal{A}\to\mathbf{Set}$ on a category $\mathcal{A}$ is a coproduct of representables precisely when each connected component of $F$'s category of elements has an initial object. Most often, this condition is imposed on a copresheaf of the form $\mathcal{B}\left(X,T-\right)$ for a functor $T\colon\mathcal{A}\to\mathcal{B}$, in which case this property says that $T$ admits generic factorizations at $X$, or equivalently that $T$ is familial at $X$. Here we generalize these results to the two-dimensional setting, replacing $\mathcal{A}$ with an arbitrary bicategory $\mathscr{A}$, and $\mathbf{Set}$ with $\mathbf{Cat}$. In this two-dimensional setting, simply asking that a pseudofunctor $F\colon\mathscr{A}\to\mathbf{Cat}$ be a coproduct of representables is often too strong of a condition. Instead, we will only ask that $F$ be a lax conical colimit of representables. This in turn allows for the weaker notion of lax generic factorizations (and lax familial representability) for pseudofunctors of bicategories $T\colon\mathscr{A}\to\mathscr{B}$. We also compare our lax familial pseudofunctors to Weber's familial 2-functors

Background: A wide range of diseases show some degree of clustering in families; family history is therefore an important aspect for clinicians when making risk predictions. Familial aggregation is often quantified in terms of a familial relative risk (FRR), and although at first glance this measure may seem simple and intuitive as an average risk prediction, its implications are not straightforward. Methods: We use two statistical models for the distribution of disease risk in a population: a dichotomous risk model that gives an intuitive understanding of the implication of a given FRR, and a continuous risk model that facilitates a more detailed computation of the inequalities in disease risk. Published estimates of FRRs are used to produce Lorenz curves and Gini indices that quantifies the inequalities in risk for a range of diseases. Results: We demonstrate that even a moderate familial association in disease risk implies a very large difference in risk between individuals in the population. We give examples of diseases for which this is likely to be true, and we further demonstrate the relationship between the point estimates of FRRs and the distribution of risk in the populat

Familial Searching is the process of searching in a DNA database for relatives of a certain individual. It is well known that in order to evaluate the genetic evidence in favour of a certain given form of relatedness between two individuals, one needs to calculate the appropriate likelihood ratio, which is in this context called a Kinship Index. Suppose that the database contains, for a given type of relative, at most one related individual. Given prior probabilities for being the relative for all persons in the database, we derive the likelihood ratio for each database member in favour of being that relative. This likelihood ratio takes all the Kinship Indices between the target individual and the members of the database into account. We also compute the corresponding posterior probabilities. We then discuss two methods to select a subset from the database that contains the relative with a known probability, or at least a useful lower bound thereof. One method needs prior probabilities and yields posterior probabilities, the other does not. We discuss the relation between the approaches, and illustrate the methods with familial searching carried out in the Dutch National DNA Datab

We investigate the consequences of adopting the criteria used by the state of California, as described by Myers et al. (2011), for conducting familial searches. We carried out a simulation study of randomly generated profiles of related and unrelated individuals with 13-locus CODIS genotypes and YFiler Y-chromosome haplotypes, on which the Myers protocol for relative identification was carried out. For Y-chromosome sharing first degree relatives, the Myers protocol has a high probability (80 - 99%) of identifying their relationship. For unrelated individuals, there is a low probability that an unrelated person in the database will be identified as a first-degree relative. For more distant Y-haplotype sharing relatives (half-siblings, first cousins, half-first cousins or second cousins) there is a substantial probability that the more distant relative will be incorrectly identified as a first-degree relative. For example, there is a 3 - 18% probability that a first cousin will be identified as a full sibling, with the probability depending on the population background. Although the California familial search policy is likely to identify a first degree relative if his profile is in t

Background: A therapeutic intervention in psychiatry can be viewed as an attempt to influence the brain's large-scale, dynamic network state transitions underlying cognition and behavior. Building on connectome-based graph analysis and control theory, Network Control Theory is emerging as a powerful tool to quantify network controllability - i.e., the influence of one brain region over others regarding dynamic network state transitions. If and how network controllability is related to mental health remains elusive. Methods: From Diffusion Tensor Imaging data, we inferred structural connectivity and inferred calculated network controllability parameters to investigate their association with genetic and familial risk in patients diagnosed with major depressive disorder (MDD, n=692) and healthy controls (n=820). Results: First, we establish that controllability measures differ between healthy controls and MDD patients while not varying with current symptom severity or remission status. Second, we show that controllability in MDD patients is associated with polygenic scores for MDD and psychiatric cross-disorder risk. Finally, we provide evidence that controllability varies with famili