搜索结果：Family relations

Cooperative play (co-play) is often positioned as a family-beneficial practice that can strengthen parent-child bonds and support parental mediation in games. Yet co-play in user-generated virtual worlds (UGVWs) can be disrupted by real-time harms that parents cannot easily prevent. Roblox, a platform with millions of user-generated virtual worlds and a large child player base, illustrates this challenge. Prior work on harmful UGVW design highlights risks beyond content problems, including manipulative monetization prompts, unmoderated social interactions, emergent in-world behaviors, and narrative designs that may normalize harmful ideologies. Current governance and moderation approaches, largely adapted from social media, focus on static artifacts and often fail to capture interactive and emergent harms in virtual worlds. This workshop paper asks: how might UGVWs and their platforms be designed to minimize harms that specifically impair family co-play experiences?

The various mass relations among members of quark and lepton families are given. Three mass relations for the charm, beauty, and top quark family members are given and three mass relations for the electron, muon, and tau lepton family members are presented.

We derive exact dynamical fluctuation-response relations (FRRs) for time-integrated observables of any nonautonomous Markov jump process. The finite-time covariance splits into an initial variability and an integral of response kernels along the driven dynamics. The identity sharpens the dynamical response thermodynamic and kinetic uncertainty relations and fluctuation-response inequalities (FRIs). It also recovers steady-state FRRs, fluctuation-dissipation theorem and Onsager reciprocity, identifies known autonomous FRIs as the zero-frequency mode.

In 1998, it was shown that, if flavor SU(3) symmetry [SU(3)$_F$] is assumed in charmless $B \to PP$ decays ($P$ is a light pseudoscalar meson), some reduced matrix elements involving electroweak penguin (EWP) operators are related to those involving tree operators. Similarly, EWP diagrams are related to tree diagrams. These SU(3)$_F$ EWP-tree relations were recently used in global analyses of $B \to PP$ decays. They have also been used over the years in analyses of the $B \to πK$ puzzle, even though the $B \to πK$ amplitudes are related by isospin symmetry [SU(2)$_I$], and not the full SU(3)$_F$. In this paper, we show that, even if only SU(2)$_I$ is assumed, there are still EWP-tree relations. In $ΔS=0$ decays, these relations are similar to those of SU(3)$_F$, and can be used to take into account the EWP contributions in the extraction of the CP phase $α$ from $B \to ππ$ decays. In $ΔS=1$ decays, the SU(2)$_I$ EWP-tree relations are quite different from those of SU(3)$_F$; when these are used to analyze the $B \to πK$ puzzle, one now finds a 4-5$σ$ discrepancy with the Standard Model, much larger than what was previously found. We argue that, if one analyzes a set of hadronic $B$

In Pawlak rough sets, the structure of the definable set families is simple and clear, but in generalizing rough sets, the structure of the definable set families is a bit more complex. There has been much research work focusing on this topic. However, as a fundamental issue in relation based rough sets, under what condition two relations induce the same definable set family has not been discussed. In this paper, based on the concept of the closure of relations, we present a necessary and sufficient condition for two relations to induce the same definable set family.

Motivated by the commitments from the Talmud in Judaism, we consider the family planning rules which require a couple to get children till certain numbers of boys and girls are reached. For example, the rabbinical school of Beit Hillel says that one boy and one girl are necessary, whereas Beit Shammai urges for two boys. Surprisingly enough, although the corresponding average family sizes differ in both cases, the gender ratios remain constant. We show more that for any family planning rule the gender ratio is equal to the birth odds. The proof of this result is given by using different mathematical techniques, such as induction principle, Doob's optional-stopping theorem, and brute-force. We conclude that, despite possible asymmetries in the religiously motivated family planning rules, they discriminate neither boys nor girls.

In this paper, we introduce the notion of a nested family of torsion pairs. We show that every stratifying system induces a nested family of torsion pairs and, conversely, that such a family together with a suitable object gives rise to a stratifying system; in particular, every stratifying system arises in this way. As an application, we present a stratifying system of infinite size that cannot be indexed by $(\mathbb{N}, \leq)$, where $\leq$ is the natural order.

Let $N$ be a positive integer. In this paper we shall study the special values of multiple polylogarithms at $N$th roots of unity, called multiple polylogarithm values (MPVs) of level $N$. These objects are generalizations of multiple zeta values and alternating Euler sums, which was studied by Euler, and more recently, many mathematicians and theoretical physicists.. Our primary goal in this paper is to investigate the relations among the MPVs of the same weight and level by using the regularized double shuffle relations, regularized distribution relations, lifted versions of such relations from lower weights, and seeded relations which are produced by relations of weight one MPVs. We call relations from the above four families \emph{standard}. Let $d(w,N)$ be the $\Q$-dimension of $\Q$-span of all MPVs of weight $w$ and level $N$. Then we obtain upper bound for $d(w,N)$ by the standard relations which in general are no worse or no better than the one given by Deligne and Goncharov depending on whether $N$ is a prime-power or not, respectively, except for 2- and 3-powers, in which case standard relations seem to be often incomplete whereas Deligne shows that their bound should be

We give a new, conceptual proof of the $\imath$Serre and Serre-Lusztig relations for $\imath$quantum groups. The key to our approach is a new formula for the comultiplication of the $\imath$-divided powers, which allows us to reformulate the relations in terms of the adjoint action. We then obtain a proof using properties of the adjoint representation. The flexibility of this approach allows us to establish a more general family of relations which seem difficult to establish otherwise.

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a novel loss function and a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family. Further, we show that our estimator can be interpreted as a solution to minimizing a particular Bregman score as well as an instance of minimizing the \textit{surrogate} likelihood. We also provide finite sample guarantees to achieve an error (in $\ell_2$-norm) of $α$ in the parameter estimation with sample compl

We derive relations among sfermion masses based on orbifold family unification models. Sfermion mass relations are specific to each model and can be useful for a selection of realistic model.

This publication presents a relation computation or calculus for international relations using a mathematical modeling. It examined trust for international relations and its calculus, which related to Bayesian inference, Dempster-Shafer theory and subjective logic. Based on an observation in the literature, we found no literature discussing the calculus method for the international relations. To bridge this research gap, we propose a relation algebra method for international relations computation. The proposed method will allow a relation computation which is previously subjective and incomputable. We also present three international relations as case studies to demonstrate the proposed method is a real-world scenario. The method will deliver the relation computation for the international relations that to support decision makers in a government such as foreign ministry, defense ministry, presidential or prime minister office. The Department of Defense (DoD) may use our method to determine a nation that can be identified as a friendly, neutral or hostile nation.

In the paper we formulate and derive the family blowup formula of family Seiberg-Witten invariants. The formula has been used in the enumerative application of counting singular curves on algebraic surfaces. We first give a topological derivation of the formula by using family index theorem. Then we define the algebraic (family) Seiberg-Witten invariants for algebraic surfaces and then give an algebraic derivation of the family blowup formula for the algebraic family Seiberg-Witten invariants.

We construct a stable homotopy type invariant for any Legendrian submanifold in a jet bundle equipped with a linear-at-infinity generating family. We show that this spectrum lifts the generating family homology groups. When the generating family extends to a generating family for an embedded Lagrangian filling, we lift the Seidel isomorphism to the spectrum level. As applications, we establish topological constraints on Lagrangian fillings arising from generating families, algebraic constraints on whether generating families admit fillings, and lower bounds on how many fiber dimensions are needed to construct a generating family for a Legendrian.

In this paper, we first construct the free Rota-Baxter family algebra generated by some set $X$ in terms of typed angularly $X$-decorated planar rooted trees. As an application, we obtain a new construction of the free Rota-Baxter algebra only in terms of angularly decorated planar rooted trees (not forests), which is quite different from the known construction via angularly decorated planar rooted forests by K. Ebrahimi-Fard and L. Guo. We then embed the free dendriform (resp. tridendriform) family algebra into the free Rota-Baxter family algebra of weight zero (resp. one). Finally, we prove that the free Rota-Baxter family algebra is the universal enveloping algebra of the free (tri)dendriform family algebra.

The Gaia Data Release 3 (DR3) contains reflectance spectra at visible wavelengths for 60,518 asteroids over the range between 374-1034 nm, representing a large sample that is well suited to studies of asteroid families. We want to assess the potential of Gaia spectra in identifying asteroid family members. Here, we focus on two L-type families, namely Tirela/Klumpkea and Watsonia. These families are known for their connection to Barbarian asteroids, which are potentially abundant in calcium-aluminum rich inclusions (CAIs). Our method is based (1) on a color taxonomy specifically built on Gaia data and (2) the similarity of spectra of candidate members with the template spectrum of a specific family. We identified objects in the halo of Tirela/Klumpkea, along with possible interlopers. We also found an independent group of eight asteroids erroneously linked to the family by the hierarchical clustering method (HCM). Consequently, the knowledge of the size distribution of the family has been significantly improved, with a more consistent shape at the larger end. The Watsonia family is a more intricate case, mainly due to its smaller size and the less marked difference between the spec

Temporal information extraction from unstructured text is essential for contextualizing events and deriving actionable insights, particularly in the medical domain. We address the task of extracting clinical events and their temporal relations using the well-studied I2B2 2012 Temporal Relations Challenge corpus. This task is inherently challenging due to complex clinical language, long documents, and sparse annotations. We introduce GRAPHTREX, a novel method integrating span-based entity-relation extraction, clinical large pre-trained language models (LPLMs), and Heterogeneous Graph Transformers (HGT) to capture local and global dependencies. Our HGT component facilitates information propagation across the document through innovative global landmarks that bridge distant entities. Our method improves the state-of-the-art with 5.5% improvement in the tempeval $F_1$ score over the previous best and up to 8.9% improvement on long-range relations, which presents a formidable challenge. We further demonstrate generalizability by establishing a strong baseline on the E3C corpus. This work not only advances temporal information extraction but also lays the groundwork for improved diagnosti

By using the Grothendieck-Riemann-Roch theorem we derive cycle relations modulo algebraic equivalence in the Jacobian of a curve. The relations generalize the relations found by Colombo and van Geemen and are analogous to but simpler than the relations recently found by Herbaut. In an appendix due to Zagier it is shown that these sets of relations are equivalent.

We formulate uncertainty relations for mutually unbiased bases and symmetric informationally complete measurements in terms of the Rényi and Tsallis entropies. For arbitrary number of mutually unbiased bases in a finite-dimensional Hilbert space, we give a family of Tsallis $α$-entropic bounds for $α\in(0;2]$. Relations in a model of detection inefficiences are obtained. In terms of Rényi's entropies, lower bounds are given for $α\in[2;\infty)$. State-dependent and state-independent forms of such bounds are both given. Uncertainty relations in terms of the min-entropy are separately considered. We also obtain lower bounds in term of the so-called symmetrized entropies. The presented results for mutually unbiased bases are extensions of some bounds previously derived in the literature. We further formulate new properties of symmetric informationally complete measurements in a finite-dimensional Hilbert space. For a given state and any SIC-POVM, the index of coincidence of generated probability distribution is exactly calculated. Short notes are made on potential use of this result in entanglement detection. Further, we obtain state-dependent entropic uncertainty relations for a sing