Effectiveness of Hindman's theorem for bounded sums

We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified finite bound. Let $\mathsf{HT}^{\leq n}_k$ denote the assertion that for each $k$-coloring $c$ of $\mathbb{N}$ there is an infinite set $X \subseteq \mathbb{N}$ such that all sums $\sum_{x \in F} x$ for $F \subseteq X$ and $0 < |F| \leq n$ have the same color. We prove that there is a computable $2$-coloring $c$ of $\mathbb{N}$ such that there is no infinite computable set $X$ such that all nonempty sums of at most $2$ elements of $X$ have the same color. It follows that $\mathsf{HT}^{\leq 2}_2$ is not provable in $\mathsf{RCA}_0$ and in fact we show that it implies $\mathsf{SRT}^2_2$ in $\mathsf{RCA}_0$. We also show that there is a computable instance of $\mathsf{HT}^{\leq 3}_3$ with all solutions computing $0'$. The proof of this result shows that $\mathsf{HT}^{\leq 3}_3$ implies $\mathsf{ACA}_0$ in $\mathsf{RCA}_0$

Interplay of buried histidine protonation and protein stability in prion misfolding

Misofolding of mammalian prion proteins (PrP) is believed to be the cause of a group of rare and fatal neurodegenerative diseases. Despite intense scrutiny however, the mechanism of the misfolding reaction remains unclear. We perform nuclear Magnetic Resonance and thermodynamic stability measurements on the C-terminal domains (residues 90–231) of two PrP variants exhibiting different pH-induced susceptibilities to aggregation: the susceptible hamster prion (GHaPrP) and its less susceptible rabbit homolog (RaPrP). The pKa of histidines in these domains are determined from titration experiments, and proton-exchange rates are measured at pH 5 and pH 7. A single buried highly conserved histidine, H187/H186 in GHaPrP/RaPrP, exhibited a markedly down shifted pKa ~5 for both proteins. However, noticeably larger pH-induced shifts in exchange rates occur for GHaPrP versus RaPrP. Analysis of the data indicates that protonation of the buried histidine destabilizes both PrP variants, but produces a more drastic effect in the less stable GHaPrP. This interpretation is supported by urea denaturation experiments performed on both PrP variants at neutral and low pH, and correlates with the difference in disease susceptibility of the two species, as expected from the documented linkage between destabilization of the folded state and formation of misfolded and aggregated species

Redistribution of the Lamin B1 genomic binding profile affects rearrangement of heterochromatic domains and SAHF formation during senescence.

Senescence is a stress-responsive form of stable cell cycle exit. Senescent cells have a distinct gene expression profile, which is often accompanied by the spatial redistribution of heterochromatin into senescence-associated heterochromatic foci (SAHFs). Studying a key component of the nuclear lamina lamin B1 (LMNB1), we report dynamic alterations in its genomic profile and their implications for SAHF formation and gene regulation during senescence. Genome-wide mapping reveals that LMNB1 is depleted during senescence, preferentially from the central regions of lamina-associated domains (LADs), which are enriched for Lys9 trimethylation on histone H3 (H3K9me3). LMNB1 knockdown facilitates the spatial relocalization of perinuclear H3K9me3-positive heterochromatin, thus promoting SAHF formation, which could be inhibited by ectopic LMNB1 expression. Furthermore, despite the global reduction in LMNB1 protein levels, LMNB1 binding increases during senescence in a small subset of gene-rich regions where H3K27me3 also increases and gene expression becomes repressed. These results suggest that LMNB1 may contribute to senescence in at least two ways due to its uneven genome-wide redistribution: first, through the spatial reorganization of chromatin and, second, through gene repression

The complex interplay between endoplasmic reticulum stress and the NLRP3 inflammasome: a potential therapeutic target for inflammatory disorders.

Inflammation is the result of a complex network of cellular and molecular interactions and mechanisms that facilitate immune protection against intrinsic and extrinsic stimuli, particularly pathogens, to maintain homeostasis and promote tissue healing. However, dysregulation in the immune system elicits excess/abnormal inflammation resulting in unintended tissue damage and causes major inflammatory diseases including asthma, chronic obstructive pulmonary disease, atherosclerosis, inflammatory bowel diseases, sarcoidosis and rheumatoid arthritis. It is now widely accepted that both endoplasmic reticulum (ER) stress and inflammasomes play critical roles in activating inflammatory signalling cascades. Notably, evidence is mounting for the involvement of ER stress in exacerbating inflammasome-induced inflammatory cascades, which may provide a new axis for therapeutic targeting in a range of inflammatory disorders. Here, we comprehensively review the roles, mechanisms and interactions of both ER stress and inflammasomes, as well as their interconnected relationships in inflammatory signalling cascades. We also discuss novel therapeutic strategies that are being developed to treat ER stress- and inflammasome-related inflammatory disorders

Human hippocampal CA3 damage disrupts both recent and remote episodic memories

Neocortical-hippocampal interactions support new episodic (event) memories, but there is conflicting evidence about the dependence of remote episodic memories on the hippocampus. In line with systems consolidation and computational theories of episodic memory, evidence from model organisms suggests that the cornu ammonis 3 (CA3) hippocampal subfield supports recent, but not remote, episodic retrieval. In this study, we demonstrated that recent and remote memories were susceptible to a loss of episodic detail in human participants with focal bilateral damage to CA3. Graph theoretic analyses of 7.0-Tesla resting-state fMRI data revealed that CA3 damage disrupted functional integration across the medial temporal lobe (MTL) subsystem of the default network. The loss of functional integration in MTL subsystem regions was predictive of autobiographical episodic retrieval performance. We conclude that human CA3 is necessary for the retrieval of episodic memories long after their initial acquisition and functional integration of the default network is important for autobiographical episodic memory performance

fMRI evidence of ‘mirror’ responses to geometric shapes

Mirror neurons may be a genetic adaptation for social interaction [1]. Alternatively, the associative hypothesis [2], [3] proposes that the development of mirror neurons is driven by sensorimotor learning, and that, given suitable experience, mirror neurons will respond to any stimulus. This hypothesis was tested using fMRI adaptation to index populations of cells with mirror properties. After sensorimotor training, where geometric shapes were paired with hand actions, BOLD response was measured while human participants experienced runs of events in which shape observation alternated with action execution or observation. Adaptation from shapes to action execution, and critically, observation, occurred in ventral premotor cortex (PMv) and inferior parietal lobule (IPL). Adaptation from shapes to execution indicates that neuronal populations responding to the shapes had motor properties, while adaptation to observation demonstrates that these populations had mirror properties. These results indicate that sensorimotor training induced populations of cells with mirror properties in PMv and IPL to respond to the observation of arbitrary shapes. They suggest that the mirror system has not been shaped by evolution to respond in a mirror fashion to biological actions; instead, its development is mediated by stimulus-general processes of learning within a system adapted for visuomotor control

FUS-ALS mutants alter FMRP phase separation equilibrium and impair protein translation

FUsed in Sarcoma (FUS) is a multifunctional RNA binding protein (RBP). FUS mutations lead to its cytoplasmic mislocalization and cause the neurodegenerative disease amyotrophic lateral sclerosis (ALS). Here, we use mouse and human models with endogenous ALS-associated mutations to study the early consequences of increased cytoplasmic FUS. We show that in axons, mutant FUS condensates sequester and promote the phase separation of fragile X mental retardation protein (FMRP), another RBP associated with neurodegeneration. This leads to repression of translation in mouse and human FUS-ALS motor neurons and is corroborated in vitro, where FUS and FMRP copartition and repress translation. Last, we show that translation of FMRP-bound RNAs is reduced in vivo in FUS-ALS motor neurons. Our results unravel new pathomechanisms of FUS-ALS and identify a novel paradigm by which mutations in one RBP favor the formation of condensates sequestering other RBPs, affecting crucial biological functions, such as protein translation

Evaluation of Mode I Fracture Toughness Assisted by the Numerical Determination of K-Resistance

The fracture toughness of a rock often varies depending on the specimen shape and the loading type used to measure it. To investigate the mode I fracture toughness using semi-circular bend (SCB) specimens, we experimentally studied the fracture toughness using SCB and chevron bend (CB) specimens, the latter being one of the specimens used extensively as an International Society for Rock Mechanics (ISRM) suggested method, for comparison. The mode I fracture toughness measured using SCB specimens is lower than both the level I and level II fracture toughness values measured using CB specimens. A numerical study based on discontinuum mechanics was conducted using a two-dimensional distinct element method (DEM) for evaluating crack propagation in the SCB specimen during loading. The numerical results indicate subcritical crack growth as well as sudden crack propagation when the load reaches the maximum. A K-resistance curve is drawn using the crack extension and the load at the point of evaluation. The fracture toughness evaluated by the K-resistance curve is in agreement with the level II fracture toughness measured using CB specimens. Therefore, the SCB specimen yields an improved value for fracture toughness when the increase of K-resistance with stable crack propagation is considered

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page

Clinical and physiological effects of transcranial electrical stimulation position on motor evoked potentials in scoliosis surgery

<p>Abstract</p> <p>Background</p> <p>During intraoperative monitoring for scoliosis surgery, we have previously elicited ipsilateral and contralateral motor evoked potentials (MEP) with cross scalp stimulation. Ipsilateral MEPs, which may have comprised summation of early ipsilaterally conducted components and transcallosally or deep white matter stimulated components, can show larger amplitudes than those derived purely from contralateral motor cortex stimulation. We tested this hypothesis using two stimulating positions. We compared intraoperative MEPs in 14 neurologically normal subjects undergoing scoliosis surgery using total intravenous anesthetic regimens.</p> <p>Methods</p> <p>Trancranial electrical stimulation was applied with both cross scalp (C3C4 or C4C3) or midline (C3Cz or C4Cz) positions. The latter was assumed to be more focal and result in little transcallosal/deep white matter stimulation. A train of 5 square wave stimuli 0.5 ms in duration at up to 200 mA was delivered with 4 ms (250 Hz) interstimulus intervals. Averaged supramaximal MEPs were obtained from the tibialis anterior bilaterally.</p> <p>Results</p> <p>The cross scalp stimulating position resulted in supramaximal MEPs that were of significantly higher amplitude, shorter latency and required lower stimulating intensity to elicit overall (Wilcoxon Signed Rank test, p < 0.05 for all), as compared to the midline stimulating position. However, no significant differences were found for all 3 parameters comparing ipsilaterally and contralaterally recorded MEPs (p > 0.05 for all), seen for both stimulating positions individually.</p> <p>Conclusions</p> <p>Our findings suggest that cross scalp stimulation resulted in MEPs obtained ipsilaterally and contralaterally which may be contributed to by summation of ipsilateral and simultaneous transcallosally or deep white matter conducted stimulation of the opposite motor cortex. Use of this stimulating position is advocated to elicit MEPs under operative circumstances where anesthetic agents may cause suppression of cortical and spinal excitability. Although less focal in nature, cross scalp stimulation would be most suitable for infratentorial or spinal surgery, in contrast to supratentorial neurosurgical procedures.</p