Rainbow sets in the intersection of two matroids

Given sets $F_1, \ldots ,F_n$, a {\em partial rainbow function} is a partial choice function of the sets $F_i$. A {\em partial rainbow set} is the range of a partial rainbow function. Aharoni and Berger \cite{AhBer} conjectured that if $M$ and $N$ are matroids on the same ground set, and $F_1, \ldots ,F_n$ are pairwise disjoint sets of size $n$ belonging to $M \cap N$, then there exists a rainbow set of size $n-1$ belonging to $M \cap N$. Following an idea of Woolbright and Brower-de Vries-Wieringa, we prove that there exists such a rainbow set of size at least $n-\sqrt{n}$

2-covers of wide Young diagrams

A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is filled injectively with the numbers $1, \ldots ,a_i$, where $a_i$ is the length of $i$th row of $Y$, and every column is also filled injectively. A conjecture of Chow and Taylor, publicized by Chow, Fan, Goemans, and Vondrak is that a wide Young diagram is Latin. We prove a dual version of the conjecture.Comment: 17 pages; Added a few more questions and a referenc

Splenic infarction: an update on William Osler\u27s observations.

BACKGROUND: Osler taught that splenic infarction presents with left upper abdominal quadrant pain, tenderness and swelling accompanied by a peritoneal friction rub. Splenic infarction is classically associated with bacterial endocarditis and sickle cell disease. OBJECTIVES: To describe the contemporary experience of splenic infarction. METHODS: We conducted a chart review of inpatients diagnosed with splenic infarction in a Jerusalem hospital between 1990 and 2003. RESULTS: We identified 26 cases with a mean age of 52 years. Common causes were hematologic malignancy (six cases) and intracardiac thrombus (five cases). Only three cases were associated with bacterial endocarditis. In 21 cases the splenic infarction brought a previously undiagnosed underlying disease to attention. Only half the subjects complained of localized left-sided abdominal pain, 36% had left-sided abdominal tenderness; 31% had no signs or symptoms localized to the splenic area, 36% had fever, 56% had leukocytosis and 71% had elevated lactate dehydrogenase levels. One splenectomy was performed and all patients survived to discharge. A post hoc analysis demonstrated that single infarcts were more likely to be associated with fever (20% vs. 63%, p \u3c 0.05) and leukocytosis (75% vs. 33%, P = 0.06) CONCLUSIONS: The clinical presentation of splenic infarction in the modern era differs greatly from the classical teaching, regarding etiology, signs and symptoms. In patients with unexplained splenic infarction, investigation frequently uncovers a new underlying diagnosis

Circuit Investigations With Open-Source Miniaturized Microscopes: Past, Present and Future

The ability to simultaneously image the spatiotemporal activity signatures from many neurons during unrestrained vertebrate behaviors has become possible through the development of miniaturized fluorescence microscopes, or miniscopes, sufficiently light to be carried by small animals such as bats, birds and rodents. Miniscopes have permitted the study of circuits underlying song vocalization, action sequencing, head-direction tuning, spatial memory encoding and sleep to name a few. The foundation for these microscopes has been laid over the last two decades through academic research with some of this work resulting in commercialization. More recently, open-source initiatives have led to an even broader adoption of miniscopes in the neuroscience community. Open-source designs allow for rapid modification and extension of their function, which has resulted in a new generation of miniscopes that now permit wire-free or wireless recording, concurrent electrophysiology and imaging, two-color fluorescence detection, simultaneous optical actuation and read-out as well as wide-field and volumetric light-field imaging. These novel miniscopes will further expand the toolset of those seeking affordable methods to probe neural circuit function during naturalistic behaviors. Here, we will discuss the early development, present use and future potential of miniscopes

Multifocal Fluorescence Microscope for Fast Optical Recordings of Neuronal Action Potentials

AbstractIn recent years, optical sensors for tracking neural activity have been developed and offer great utility. However, developing microscopy techniques that have several kHz bandwidth necessary to reliably capture optically reported action potentials (APs) at multiple locations in parallel remains a significant challenge. To our knowledge, we describe a novel microscope optimized to measure spatially distributed optical signals with submillisecond and near diffraction-limit resolution. Our design uses a spatial light modulator to generate patterned illumination to simultaneously excite multiple user-defined targets. A galvanometer driven mirror in the emission path streaks the fluorescence emanating from each excitation point during the camera exposure, using unused camera pixels to capture time varying fluorescence at rates that are ∼1000 times faster than the camera’s native frame rate. We demonstrate that this approach is capable of recording Ca2+ transients resulting from APs in neurons labeled with the Ca2+ sensor Oregon Green Bapta-1 (OGB-1), and can localize the timing of these events with millisecond resolution. Furthermore, optically reported APs can be detected with the voltage sensitive dye DiO-DPA in multiple locations within a neuron with a signal/noise ratio up to ∼40, resolving delays in arrival time along dendrites. Thus, the microscope provides a powerful tool for photometric measurements of dynamics requiring submillisecond sampling at multiple locations

Rrm3 and Pif1 division of labor during replication through leading and lagging strand G-quadruplex

Members of the conserved Pif1 family of 5\u27-3\u27 DNA helicases can unwind G4s and mitigate their negative impact on genome stability. In Saccharomyces cerevisiae, two Pif1 family members, Pif1 and Rrm3, contribute to the suppression of genomic instability at diverse regions including telomeres, centromeres and tRNA genes. While Pif1 can resolve lagging strand G4s in vivo, little is known regarding Rrm3 function at G4s and its cooperation with Pif1 for G4 replication. Here, we monitored replication through G4 sequences in real time to show that Rrm3 is essential for efficient replisome progression through G4s located on the leading strand template, but not on the lagging strand. We found that Rrm3 importance for replication through G4s is dependent on its catalytic activity and its N-terminal unstructured region. Overall, we show that Rrm3 and Pif1 exhibit a division of labor that enables robust replication fork progression through leading and lagging strand G4s, respectively

A shared neural ensemble links distinct contextual memories encoded close in time.

Recent studies suggest that a shared neural ensemble may link distinct memories encoded close in time. According to the memory allocation hypothesis, learning triggers a temporary increase in neuronal excitability that biases the representation of a subsequent memory to the neuronal ensemble encoding the first memory, such that recall of one memory increases the likelihood of recalling the other memory. Here we show in mice that the overlap between the hippocampal CA1 ensembles activated by two distinct contexts acquired within a day is higher than when they are separated by a week. Several findings indicate that this overlap of neuronal ensembles links two contextual memories. First, fear paired with one context is transferred to a neutral context when the two contexts are acquired within a day but not across a week. Second, the first memory strengthens the second memory within a day but not across a week. Older mice, known to have lower CA1 excitability, do not show the overlap between ensembles, the transfer of fear between contexts, or the strengthening of the second memory. Finally, in aged mice, increasing cellular excitability and activating a common ensemble of CA1 neurons during two distinct context exposures rescued the deficit in linking memories. Taken together, these findings demonstrate that contextual memories encoded close in time are linked by directing storage into overlapping ensembles. Alteration of these processes by ageing could affect the temporal structure of memories, thus impairing efficient recall of related information

Distributions of switching times of single-domain particles using a time quantified Monte Carlo method

Using a time quantified Monte Carlo scheme we performed simulations of the switching time distribution of single mono-domain particles in the Stoner-Wohlfarth approximation. We considered uniaxial anisotropy and different conditions for the external applied field. The results obtained show the switching time distribution can be well described by two relaxation times, either when the applied field is parallel to the easy axis or for an oblique external field and a larger damping constant. We found that in the low barrier limit these relaxation times are in very good agreement with analytical results obtained from solutions of the Fokker-Planck equation related to this problem. When the damping is small and the applied field is oblique the shape of the distribution curves shows several peaks and resonance effects.Comment: 12 pages, 5 figures. New references, changes in the title and minor correction