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

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

Printing surface charge as a new paradigm to program droplet transport

Directed, long-range and self-propelled transport of droplets on solid surfaces, especially on water repellent surfaces, is crucial for many applications from water harvesting to bio-analytical devices. One appealing strategy to achieve the preferential transport is to passively control the surface wetting gradients, topological or chemical, to break the asymmetric contact line and overcome the resistance force. Despite extensive progress, the directional droplet transport is limited to small transport velocity and short transport distance due to the fundamental trade-off: rapid transport of droplet demands a large wetting gradient, whereas long-range transport necessitates a relatively small wetting gradient. Here, we report a radically new strategy that resolves the bottleneck through the creation of an unexplored gradient in surface charge density (SCD). By leveraging on a facile droplet printing on superamphiphobic surfaces as well as the fundamental understanding of the mechanisms underpinning the creation of the preferential SCD, we demonstrate the self-propulsion of droplets with a record-high velocity over an ultra-long distance without the need for additional energy input. Such a Leidenfrost-like droplet transport, manifested at ambient condition, is also genetic, which can occur on a variety of substrates such as flexible and vertically placed surfaces. Moreover, distinct from conventional physical and chemical gradients, the new dimension of gradient in SCD can be programmed in a rewritable fashion. We envision that our work enriches and extends our capability in the manipulation of droplet transport and would find numerous potential applications otherwise impossible.Comment: 11 pages, 4 figure

Mitochondrial Perturbation in Alzheimer’s Disease and Diabetes

Mitochondria are well-known cellular organelles that play a vital role in cellular bioenergetics, heme biosynthesis, thermogenesis, calcium homeostasis, lipid catabolism, and other metabolic activities. Given the extensive role of mitochondria in cell function, mitochondrial dysfunction plays a part in many diseases, including diabetes and Alzheimer’s disease (AD). In most cases, there is overwhelming evidence that impaired mitochondrial function is a causative factor in these diseases. Studying mitochondrial function in diseased cells vs healthy cells may reveal the modified mechanisms and molecular components involved in specific disease states. In this chapter, we provide a concise overview of the major recent findings on mitochondrial abnormalities and their link to synaptic dysfunction relevant to neurodegeneration and cognitive decline in AD and diabetes. Our increased understanding of the role of mitochondrial perturbation indicates that the development of specific small molecules targeting aberrant mitochondrial function could provide therapeutic benefits for the brain in combating aging-related dementia and neurodegenerative diseases by powering up brain energy and improving synaptic function and transmission

Combination of carbon nanotubes and two-photon absorbers for broadband optical limiting

New systems are required for optical limiting against broadband laser pulses. We demonstrate that the association of non-linear scattering from single-wall carbon nanotubes (SWNT) and multiphoton absorption (MPA) from organic chromophores is a promising approach to extend performances of optical limiters over broad spectral and temporal ranges. Such composites display high linear transmission and good neutral colorimetry and are particularly efficient in the nanosecond regime due to cumulative effects.Comment: 5 avril 200

Incorporating Physical Information into Clustering for FPGAs

The traditional approach to FPGA clustering and CLB-level placement has been shown to yield significantly worse overall placement quality than approaches which allow BLEs to move during placement. In practice, however, modern FPGA architectures require computationally-expensive Design Rule Checks (DRC) which render BLE-level placement impractical. This thesis research addresses this problem by proposing a novel clustering framework that produces better initial clusters that help to reduce the dependence on BLE-level placement. The work described in this dissertation includes: (1) a comparison of various clustering algorithms used for FPGAs, (2) the introduction of a novel hybridized clustering framework for timing-driven FPGA clustering, (3) the addition of physical information to make better clusters, (4) a comparison of the implemented approaches to known clustering tools, and (5) the implementation and evaluation of cluster improvement heuristics. The proposed techniques are quantified across accepted benchmarks and show that the implemented DPack produces results with 16% less wire length, 19% smaller minimum channel widths, and 8% less critical delay, on average, than known academic tools. The hybridized approach, HDPack, is found to achieve 21% less wire length, 24% smaller minimum channel widths, and 6% less critical delay, on average

Monitoring Genomic Sequences during SELEX Using High-Throughput Sequencing: Neutral SELEX

Background: SELEX is a well established in vitro selection tool to analyze the structure of ligand-binding nucleic acid sequences called aptamers. Genomic SELEX transforms SELEX into a tool to discover novel, genomically encoded RNA or DNA sequences binding a ligand of interest, called genomic aptamers. Concerns have been raised regarding requirements imposed on RNA sequences undergoing SELEX selection. Methodology/Principal Findings: To evaluate SELEX and assess the extent of these effects, we designed and performed a Neutral SELEX experiment omitting the selection step, such that the sequences are under the sole selective pressure of SELEX’s amplification steps. Using high-throughput sequencing, we obtained thousands of full-length sequences from the initial genomic library and the pools after each of the 10 rounds of Neutral SELEX. We compared these to sequences obtained from a Genomic SELEX experiment deriving from the same initial library, but screening for RNAs binding with high affinity to the E. coli regulator protein Hfq. With each round of Neutral SELEX, sequences became less stable and changed in nucleotide content, but no sequences were enriched. In contrast, we detected substantial enrichment in the Hfq-selected set with enriched sequences having structural stability similar to the neutral sequences but with significantly different nucleotide selection. Conclusions/Significance: Our data indicate that positive selection in SELEX acts independently of the neutral selectiv