On Atkin-Swinnerton-Dyer congruence relations

In this paper we exhibit a noncongruence subgroup \G whose space of weight 3 cusp forms S_3(\G) admits a basis satisfying the Atkin-Swinnerton-Dyer congruence relations with two weight 3 newforms for certain congruence subgroups. This gives a modularity interpretation of the motive attached to S_3(\G) by A. Scholl and also verifies the Atkin-Swinnerton-Dyer congruence conjecture for this space.Comment: 25 page

SOCIAL WORKERS\u27 PERCEPTION ON THE NEEDS AND SERVICES FOR FOSTER CHILDREN WITH SPECIAL NEEDS

Foster children are already at a disadvantage given that they tend to live in a home without their parents. Social workers have direct interactions working with children with special needs, and through interviews with the workers, we aimed to understand whether or not the services available are able to meet foster children’s special needs. The research on special needs children in foster care is quite limited. The purpose of the study was to identify social workers’ perceptions of the needs of special needs foster children and their access to services. This study used qualitative interviews with open-ended questions to gather qualitative data from ten social worker participants. The researchers employed thematic analysis techniques to analyze the qualitative data. The themes that emerged from analyzing the data were social workers’ challenges in providing services to special needs foster children, social workers’ access to services, and the need for institutional support to effectively manage service delivery for special needs foster children. This study found that social workers face challenges in obtaining training for parents and social workers, navigating complex funding processes, managing inconsistent desires between parents and court officials, and dealing with the limited number of capable foster homes. The social workers interviewed identified different tactics that could be implemented in order to improve services for the special needs foster children through changes and improvements within the department. Understanding large-scale policy and practice issues, such as organizational change or resource management, can lead county agency social workers to advocate for the challenges of special needs children in child welfare

Synchronization in the quaternionic Kuramoto model

In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we analyze the case when the coupling strength is weak. For $N=2$, when coupling strength is weak (below the critical coupling strength $\lambda_c$), we show that new periodic orbits emerge near each equilibrium point, and hence phase-locking state exists. This phenomenon is different from the real Kuramoto system since it is impossible to arrive at any synchronization when $\lambda<\lambda_c$. A theorem is proved which states that the closed contours form a set of "Baumkuchen" that is dense near each equilibrium point. In other words, the trajectory of phase difference lies on a $4D$-torus surface. Therefore, this implies that the phase-locking state is Lyapunov stable but not asymptotically stable. The proof uses a new infinite buffer method ("$\delta/n$ criterion") and a Lyapunov function argument. This has been studied both analytically and numerically. For $N=3$, we consider Lion Dance flow, the analog of Cherry flow, to demonstrate that the quaternionic synchronization exists even when the coupling strength is "super weak" (when $\lambda/\omega 3$, the stable manifold of Lion Dance flow exists, and the number of these equilibria is $\lfloor \frac{N-1}{2}\rfloor$. Therefore, we conjecture that quaternionic synchronization always exists.Comment: 35 pages, 6 figure

Immunotherapy for Lung Cancers

Lung cancer is the leading cause of cancer-related deaths worldwide. Although treatment methods in surgery, irradiation, and chemotherapy have improved, prognosis remains unsatisfactory and developing new therapeutic strategies is still an urgent demand. Immunotherapy is a novel therapeutic approach wherein activated immune cells can specifically kill tumor cells by recognition of tumor-associated antigens without damage to normal cells. Several lung cancer vaccines have demonstrated prolonged survival time in phase II and phase III trials, and several clinical trials are under investigation. However, many clinical trials involving cancer vaccination with defined tumor antigens work in only a small number of patients. Cancer immunotherapy is not completely effective in eradicating tumor cells because tumor cells escape from host immune scrutiny. Understanding of the mechanism of immune evasion regulated by tumor cells is required for the development of more effective immunotherapeutic approaches against lung cancer. This paper discusses the identification of tumor antigens in lung cancer, tumor immune escape mechanisms, and clinical vaccine trials in lung cancer

Cerebral small vessel disease burden is associated with poststroke depressive symptoms: A 15-month prospective study

Objective: All types of cerebral small vessel disease (SVD) markers including lacune, white matter hyperintensities (WMH), cerebral microbleeds, and perivascular spaces were found to be associated with poststroke depressive symptoms (PDS). This study explored whether the combination of the four markers constituting an overall SVD burden was associated with PDS. Methods: A cohort of 563 patients with acute ischemic stroke were followed over a 15-month period after the index stroke. A score of _7 on the 15-item Geriatric Depression Scale was defined as clinically significant PDS. Scores of the four SVD markers ascertained on magnetic resonance imaging were summed up to represent total SVD burden. The association between SVD burden and PDS was assessed with generalized estimating equation models. Results: The study sample had a mean age of 67.0 _ 10.2 years and mild-moderate stroke [National Institutes of Health Stroke Scale score: 3, interquartile, 1–5]. PDS were found in 18.3%, 11.6%, and 12.3% of the sample at 3, 9, and 15 months after stroke, respectively. After adjusting for demographic characteristics, vascular risk factors, social support, stroke severity, physical and cognitive functions, and size and locations of stroke, the SVD burden was associated with an increased risk of PDS [odds ratio = 1.30; 95% confidence interval = 1.07–1.58; p = 0.010]. Other significant predictors of PDS were time of assessment, female sex, smoking, number of acute infarcts, functional independence, and social support. Conclusion: SVD burden was associated with PDS examined over a 15-month follow-up in patients with mild to moderate acute ischemic stroke

Seiberg duality, quiver gauge theories, and Ihara's zeta function

We study Ihara’s zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara’s zeta function to be the generating function for the generic superpotential of the gauge theory

Neural Functional Transformers

The recent success of neural networks as implicit representation of data has driven growing interest in neural functionals: models that can process other neural networks as input by operating directly over their weight spaces. Nevertheless, constructing expressive and efficient neural functional architectures that can handle high-dimensional weight-space objects remains challenging. This paper uses the attention mechanism to define a novel set of permutation equivariant weight-space layers and composes them into deep equivariant models called neural functional Transformers (NFTs). NFTs respect weight-space permutation symmetries while incorporating the advantages of attention, which have exhibited remarkable success across multiple domains. In experiments processing the weights of feedforward MLPs and CNNs, we find that NFTs match or exceed the performance of prior weight-space methods. We also leverage NFTs to develop Inr2Array, a novel method for computing permutation invariant latent representations from the weights of implicit neural representations (INRs). Our proposed method improves INR classification accuracy by up to $+17\%$ over existing methods. We provide an implementation of our layers at https://github.com/AllanYangZhou/nfn

Retinal Changes in a Mutant Form of Goldfish with Megalophthalmia

The retinal changes of a mutant strain of goldfish with megalophthalmia were studied by histology, electron microscopy and biochemistry. Changes in the morphology of the pigment epithelium, decrease in number of photoreceptors, thinning out of retinal layers and the existence of spaces in the retina were all features as the eyes grew in size. Invasion of macrophages was also evident in the retina. A decrease in leucine uptake per milligram of retina was also detected as the eye grew beyond 0.8 millilitre in volume. These changes, although related to volume changes (i.e., growth) of the eyes, were found to have little relationship with increase of intraocular pressure as intraocular pressures in the growing eyes of the mutant strain did not change much. Goldfish from a control strain with similar eye volumes and sizes (ages) were used for comparison and similar changes as in the mutant were not apparent

Women's employment trajectories in a low-income setting: Stratification and change in Nepal

Background: Across the globe, employment for pay outside the home plays a key role in the lives of women, and increasing the proportion of women involved in high-quality jobs is a critical component of reaching several sustainable development goals. While existing research from high-income societies demonstrates that women's employment is not constant over the life course, relatively less is known about women's employment trajectories in low-income countries. Objective: We examine employment trajectories among women in rural Nepal, accounting for job type, employment intensity, and earnings. Methods: Using eight years of quarterly employment data from the 2016 Female Labor Force Participation and Child Outcomes Study component of the Chitwan Valley Family Study, we identify typologies of employment trajectories by conducting sequence and cluster analyses. Results: First, half of the women in our sample were never employed in the study period. Second, among women who were ever employed, there were considerable transitions into and out of the workforce. Third, women's employment trajectories are largely determined by job type (wage labor, salaried jobs, and self-employment), with little movement across job types. Additionally, self-employed women and those with salaried jobs had higher earnings and higher employment intensity than women with wage labor jobs. Conclusions: We see intense stratification into job types, including no employment at all, and substantial transitions into and out of the workforce among workers. Women experience many employment disruptions over the life course, with little sign of upward employment mobility. Contribution: This study provides new empirical portraits of women's employment in low-income settings by investigating the multiple dimensions of women's employment from a life course perspective