Query Complexity of Search Problems

We relate various complexity measures like sensitivity, block sensitivity, certificate complexity for multi-output functions to the query complexities of such functions. Using these relations, we provide the following improvements upon the known relationship between pseudo-deterministic and deterministic query complexity for total search problems: - We show that deterministic query complexity is at most the third power of its pseudo-deterministic query complexity. Previously, a fourth-power relation was shown by Goldreich, Goldwasser and Ron (ITCS\u2713). - We improve the known separation between pseudo-deterministic and randomized decision tree size for total search problems in two ways: (1) we exhibit an exp(??(n^{1/4})) separation for the SearchCNF relation for random k-CNFs. This seems to be the first exponential lower bound on the pseudo-deterministic size complexity of SearchCNF associated with random k-CNFs. (2) we exhibit an exp(?(n)) separation for the ApproxHamWt relation. The previous best known separation for any relation was exp(?(n^{1/2})). We also separate pseudo-determinism from randomness in And and (And,Or) decision trees, and determinism from pseudo-determinism in Parity decision trees. For a hypercube colouring problem, that was introduced by Goldwasswer, Impagliazzo, Pitassi and Santhanam (CCC\u2721) to analyze the pseudo-deterministic complexity of a complete problem in TFNP^{dt}, we prove that either the monotone block-sensitivity or the anti-monotone block sensitivity is ?(n^{1/3}); Goldwasser et al. showed an ?(n^{1/2}) bound for general block-sensitivity

A clinical comparative study of ropivacaine versus ropivacaine with fentanyl by continuous epidural infusion for post-operative analgesia and ambulation in patients undergoing major gynecological surgery

Background: To compare the effect of continuous epidural infusion of ropivacaine versus ropivacaine-fentanyl for post-operative analgesia and ambulation in patients undergoing major gynaecological surgeries.Methods: A total of 60 patients of age 20 to 50 yrs of body mass index (BMI) within normal range (18.5to24.9 kg/m2) posted for major gynecological surgeries were divided into two equal groups (Group R and RF) in a prospective, randomized, double-blind fashion. In Group RF (n=30) 0.1% Ropivacaine with 2µg/ml Fentanyl and in Group R (n =30) 0.1% ropivacaine were used. General anaesthesia was given to all patients. Continuous epidural infusion using elastomeric pump was started at ‘0’ post-operative hours at 6ml/hour. Post -operative pain (Visual Analogue Scale Score), ambulation (James Modified Bromage Scale) and side effects were noted at 0, 2, 4, 6, 12, 18, 24, 36 and 48hrs.Results: The differences in VAS Score of subjects of both the groups were statistically significant(p<0.05) at 18 hrs, 24hrs, 36hrs and 48 hrs and the differences in Modified Bromage Scale of subjects of the groups were statistically similar at most of the time intervals. Also, the side effects were statistically similar between the groups.Conclusions: Author concluded that ropivacaine-fentanyl is better than ropivacaine alone by continuous epidural infusion for post-operative analgesia in major gynecological surgeries with no statistically significant side effects, effect on ambulation being similar in both the groups

Nod2 Downregulates TLR2/1 Mediated IL1β Gene Expression in Mouse Peritoneal Macrophages

Nod2 is a cytosolic pattern recognition receptor. It has been implicated in many inflammatory conditions. Its signaling has been suggested to modulate TLR responses in a variety of ways, yet little is known about the mechanistic details of the process. We show in this study that Nod2 knockdown mouse peritoneal macrophages secrete more IL1β than normal macrophages when stimulated with peptidoglycan (PGN). Muramyl dipeptide (MDP, a Nod2 ligand) + PGN co-stimulated macrophages have lower expression of IL1β than PGN (TLR2/1 ligand) stimulated macrophages. MDP co-stimulation have similar effects on Pam3CSK4 (synthetic TLR2/1 ligand) mediated IL1β expression suggesting that MDP mediated down regulating effects are receptor dependent and ligand independent. MDP mediated down regulation was specific for TLR2/1 signaling as MDP does not affect LPS (TLR4 ligand) or zymosan A (TLR2/6 ligand) mediated IL1β expression. Mechanistically, MDP exerts its down regulating effects by lowering PGN/Pam3CSK4 mediated nuclear cRel levels. Lower nuclear cRel level were observed to be because of enhanced transporting back rather than reduced nuclear translocation of cRel in MDP + PGN stimulated macrophages. These results demonstrate that Nod2 and TLR2/1 signaling pathways are independent and do not interact at the level of MAPK or NF-κB activation

Mycobacterium indicus pranii Supernatant Induces Apoptotic Cell Death in Mouse Peritoneal Macrophages In Vitro

Mycobacterium indicus pranii (MIP), also known as Mw, is a saprophytic, non-pathogenic strain of Mycobacterium and is commercially available as a heat-killed vaccine for leprosy and recently tuberculosis (TB) as part of MDT. In this study we provide evidence that cell-free supernatant collected from original MIP suspension induces rapid and enhanced apoptosis in mouse peritoneal macrophages in vitro. It is demonstrated that the MIP cell-free supernatant induced apoptosis is mitochondria-mediated and caspase independent and involves mitochondrial translocation of Bax and subsequent release of AIF and cytochrome c from the mitochondria. Experiments with pharmacological inhibitors suggest a possible role of PKC in mitochondria-mediated apoptosis of macrophages

Discovering Response-Eliciting Factors in Social Question Answering : A Reddit Inspired Study

Questions form an integral part of our everyday communication, both offline and online. Getting responses to our questions from others is fundamental to satisfying our information need and in extending our knowledge boundaries. A question may be represented using various factors such as social, syntactic, semantic, etc. We hypothesize that these factors contribute with varying degrees towards getting responses from others for a given question. We perform a thorough empirical study to measure effects of these factors using a novel question and answer dataset from the website Reddit.com. We also use a sparse non-negative matrix factorization technique to automatically induce interpretable semantic factors from the question dataset. Such interpretable factor-based analysis overcomes limitations faced by prior related research. We also document various patterns on response prediction we observe during our analysis. For instance, we found that preference-probing questions are rarely answered by actors

Randomized versus Deterministic Decision Tree Size

A classic result of Nisan [SICOMP '91] states that the deterministic decision tree∗depth∗complexity of every total Boolean function is at most the cube of its randomized decision tree∗depth∗complexity. The question whether randomness helps in significantly reducing the∗size∗of decision trees appears not to have been addressed. We show that the logarithm of the deterministic decision tree size complexity of every total Boolean function on n input variables is at most the fourth power of the logarithm of its bounded-error randomized decision tree size complexity, ignoring a polylogarithmic factor in the input size. Our result has the following consequences:-The deterministic AND-OR query complexity of a total Boolean function is at most the fourth power of its randomized AND-OR query complexity, ignoring a polylog n factor.-The deterministic AND (OR) query complexity of a total Boolean function is at most the cube of its randomized AND (OR) query complexity, ignoring a polylog n factor. This answers a recent open question posed by Knop, Lovett, McGuire and Yuan [SIGACT News '21].-The notion of∗rank∗of a Boolean function was defined in a classic work of Ehrenfeucht and Haussler [Information and Computation'89] in the context of learning theory, and is characterized by the logarithm of decision tree size up to a logarithmic factor in the input size. Our results confirm a recent conjecture (ignoring a polylog n factor) of Cornelissen, Mande and Patro [FSTTCS '22], that asserted the equivalence of randomized and deterministic analogs of rank, upto polynomial factors, for all total Boolean functions.-Combined with the above-mentioned work of Ehrenfeucht and Haussler, our result implies that the class of functions computable by randomized decision trees of polynomial size, is PAC-learnable in quasi-polynomial time. To obtain our main result on decision tree size, we use as an intermediate measure the∗block number∗of a Boolean function, studied first by Kulkarni and Tal [CJTCS'16], which can be thought of as a counting analog of∗block sensitivity∗of a Boolean function that played a central role in Nisan's result mentioned above

Differential modulation of PGN mediated gene expression by MDP co-stimulation.

<p>(<b>A</b>) ELISA for IL10, TNFα and RANTES. Normal of Nod2 knockout or scrambled sequence siRNA treated macrophages were stimulated for 12 hours with various ligands as indicated. Culture supernatant was checked for the presence of indicated cytokines. Results are presented as the mean of triplicate wells ± SD. Data is plotted on split semi-log graph. Statistical significance was checked by two way ANOVA. P value was found to be significant (<0.0001). (<b>B</b>) Western blot analysis of iNOS and COX2. Macrophages were stimulated for 6 hours as indicated and whole cell lysates were checked for the presence of iNOS and COX2 proteins. Results correspond to one representative experiment of three independent experiments.</p

MDP co-stimulation facilitates export of nuclear cRel subunits in PGN stimulated macrophages.

<p>(<b>A-E</b>), (<b>A</b>) Nuclear translocation of cRel. Normal or cycloheximide (5 µg/ml) pre-treated (20 minutes prior to PGN or MDP+PGN stimulus) macrophages were stimulated for 40 minutes as indicated. Nuclear extracts were prepared and run on 10% SDS-PAGE. 30 µg of nuclear extract was loaded per well. Results correspond to one representative experiment of three independent experiments. (<b>B</b>) Phosphorylation of IκB. Normal or cycloheximide (5 µg/ml) pre-treated (20 minutes prior to PGN or MDP+PGN stimulus) macrophages were stimulated for 30 minutes as indicated. Whole cell lysates were checked for the presence of phosphorylated form of IκB. Results correspond to one representative experiment of three independent experiments. (<b>C</b>) Electrophoretic mobility shift Assay for NF-κB. Macrophages were stimulated for 40 minutes as indicated. Nuclear extracts were prepared and incubated with 100 fmol of biotinylated NF-κB binding sequence. EMSA was performed as described. Cycloheximide treatment was for 20 minutes prior to PGN or MDP+PGN stimulation. Results correspond to one representative experiment of two independent experiments. (<b>D</b>) Phosphorylation of IκB. Macrophages were stimulated for 30 minutes as indicated. Whole cell lysates were checked for the presence of phosphorylated form of IκB. Results correspond to one representative experiment of three independent experiments (<b>E</b>) Activation of MAPKs. Macrophages were stimulated as indicated for 30 minutes. Cell extracts were analysed for the presence of phosphorylated (activated) forms of p38, ERK and JNK. Results shown correspond to one representative experiment of three independent experiments.</p

Cartoon diagram showing the effect of Nod2 co-stimulation on gene expression induced by different TLRs.

<p>Gene 1 and gene 2 are independently induced by different TLRs and Nod2. Different induction level upon stimulation of different receptors indicates involvement of receptor specific TF profile. Co stimulation of macrophages with MDP and TLR ligands alters the profile of TFs bound to some gene promoters resulting in modulation of expression in various ways.</p