Anti-lecture Hall Compositions and Overpartitions

We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruent to $0,\pm 1$ modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two Rogers-Ramanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage.Comment: 16 page

NameBuzzer

The NameExpert is an iOS mobile application that will help users remember the names of new acquaintances. Many people often experience situations where they would run into someone they have been introduced to before, but could not remember the name to. Situations like this tend to instigate feelings of frustration and awkwardness between both parties. Names are important as part of identity and so the NameExpert would allow individuals to connect names to things like location of the meet, appearances, and other systematic ways. The NameExpert would utilize an algorithm that is derived from a proven psychological research regarding the human memory to help the individual retain the new names

The Rogers-Ramanujan-Gordon Theorem for Overpartitions

Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that $B_{k,i}(n)=A_{k,i}(n)$. Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases $i=1$ and $i=k$. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let $D_{k,i}(n)$ be the number of overpartitions of $n$ satisfying certain difference condition and $C_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruences condition. We show that $C_{k,i}(n)=D_{k,i}(n)$. By using a function introduced by Andrews, we obtain a recurrence relation which implies that the generating function of $D_{k,i}(n)$ equals the generating function of $C_{k,i}(n)$. We also find a generating function formula of $D_{k,i}(n)$ by using Gordon marking representations of overpartitions, which can be considered as an overpartition analogue of an identity of Andrews for ordinary partitions.Comment: 26 page

B\"uchi VASS recognise w-languages that are Sigma^1_1 - complete

This short note exhibits an example of a Sigma^1_1-complete language that can be recognised by a one blind counter B\"uchi automaton (or equivalently a B\"uchi VASS with only one place)

Tipping the Scale to Bring a Balanced Approach: Evidence Disclosure in Chinese International Arbitration

Due to the ever-increasing trade between China and the rest of the world, commercial disputes have risen dramatically. Many foreign companies choose to resolve these disputes through arbitration to circumvent the Chinese courts and to retain more autonomy and control. Arbitration itself can also be a problem because rules and laws differ, depending on the jurisdiction and the institution involved. Under China’s civil law tradition, arbitrators are restricted in their ability to force parties to disclose evidence that may be detrimental to their case. Additionally, arbitrators have no authority to obtain evidence from uncooperative third parties. This Article seeks to provide some guidance for parties engaged in arbitration proceedings in China

Lessons to be Learned from Bimodal Bilingualism

This article presents a selective overview of topics related to the language experience of early bimodal bilinguals - individuals who are raised from an early age using two languages from two different modalities, typically spoken (or written) and signed. We show that deaf and hearing bimodal bilinguals may display patterns of bilingualism that are similar to unimodal bilinguals in some ways, such as the use of both languages in a single situation or even a single utterance. Nevertheless, there are also differences between bimodal and unimodal bilinguals, and differences among different subgroups of bimodal bilinguals, given large variation in relative access to the dominant and minority language(s) in their environment and their differential experiences in schooling and interactions with potential interlocutors. Moreover, we review studies discussing potential advantages of the sign modality and advantages of bilingualism in this population. We hope to highlight the importance of considering children’s overall language experience, including the age(s) at which they are exposed to each of their languages, the richness of their experiences with each of the languages, and the ways that the language-learning experience may contribute to the child’s linguistic and cognitive development

Altered sterol metabolism in budding yeast affects mitochondrial iron–sulfur (Fe-S) cluster synthesis

Ergosterol synthesis is essential for cellular growth and viability of the budding yeast Saccharomyces cerevisiae, and intracellular sterol distribution and homeostasis are therefore highly regulated in this species. Erg25 is an iron-containing C4-methyl sterol oxidase that contributes to the conversion of 4,4-dimethylzymosterol to zymosterol, a precursor of ergosterol. The ERG29 gene encodes an endoplasmic reticulum (ER)-associated protein, and here we identified a role for Erg29 in the methyl sterol oxidase step of ergosterol synthesis. ERG29 deletion resulted in lethality in respiring cells, but respiration-incompetent (Rho- or Rho0) cells survived, suggesting that Erg29 loss leads to accumulation of oxidized sterol metabolites that affect cell viability. Down-regulation of ERG29 expression in Δerg29 cells indeed led to accumulation of methyl sterol metabolites, resulting in increased mitochondrial oxidants and a decreased ability of mitochondria to synthesize iron-sulfur (Fe-S) clusters due to reduced levels of Yfh1, the mammalian frataxin homolog, which is involved in mitochondrial iron metabolism. Using a high-copy genomic library, we identified suppressor genes that permitted growth of Δerg29 cells on respiratory substrates, and these included genes encoding the mitochondrial proteins Yfh1, Mmt1, Mmt2, and Pet20, which reversed all phenotypes associated with loss of ERG29 Of note, loss of Erg25 also resulted in accumulation of methyl sterol metabolites and also increased mitochondrial oxidants and degradation of Yfh1. We propose that accumulation of toxic intermediates of the methyl sterol oxidase reaction increases mitochondrial oxidants, which affect Yfh1 protein stability. These results indicate an interaction between sterols generated by ER proteins and mitochondrial iron metabolism