353 research outputs found
More on AC^0[oplus] and Variants of the Majority Function
No full textIn this paper we prove two results about AC^0[oplus] circuits.
(1) We show that for d(N) = o(sqrt(log N/log log N)) and N {0,1}} such that
- f_N has uniform AC^0 formulas of depth d and size at most s;
- f_N does not have AC^0[oplus] formulas of depth d and size s^epsilon, where epsilon is a fixed absolute constant.
This gives a quantitative improvement on the recent result of Limaye, Srinivasan, Sreenivasaiah, Tripathi, and Venkitesh, (STOC, 2019), which proved a similar Fixed-Depth Size-Hierarchy theorem but for d << log log N and s << exp(N^(1/2^Omega(d))).
As in the previous result, we use the Coin Problem to prove our hierarchy theorem. Our main technical result is the construction of uniform size-optimal formulas for solving the coin problem with improved sample complexity (1/delta)^O(d) (down from (1/delta)^(2^O(d)) in the previous result).
(2) In our second result, we show that randomness buys depth in the AC^0[oplus] setting. Formally, we show that for any fixed constant d >= 2, there is a family of Boolean functions that has polynomial-sized randomized uniform AC^0 circuits of depth d but no polynomial-sized (deterministic) AC^0[oplus] circuits of depth d.
Previously Viola (Computational Complexity, 2014) showed that an increase in depth (by at least 2) is essential to avoid superpolynomial blow-up while derandomizing randomized AC^0 circuits. We show that an increase in depth (by at least 1) is essential even for AC^0[oplus].
As in Viola’s result, the separating examples are promise variants of the Majority function on N inputs that accept inputs of weight at least N/2 + N/(log N)^(d-1) and reject inputs of weight at most N/2 - N/(log N)^(d-1)
On the Probabilistic Degrees of Symmetric Boolean Functions
No full textThe probabilistic degree of a Boolean function f:{0,1}^n -> {0,1} is defined to be the smallest d such that there is a random polynomial P of degree at most d that agrees with f at each point with high probability. Introduced by Razborov (1987), upper and lower bounds on probabilistic degrees of Boolean functions - specifically symmetric Boolean functions - have been used to prove explicit lower bounds, design pseudorandom generators, and devise algorithms for combinatorial problems.
In this paper, we characterize the probabilistic degrees of all symmetric Boolean functions up to polylogarithmic factors over all fields of fixed characteristic (positive or zero)
Scientific Study of Amish Tripathi\u27s Novels
No full textAmish Tripathi is a rising contempory writer. His passion towards Indian mythology inspired him to write about Hindu Mythology upon Hindu God and Goddesses. He is one of the best selling author in English literature, written about mythological stories. All the novels of Amish Tripathi are modernized in such a way that it can match with the interest of today\u27s generation. His novels are about society, women, oppressed classed etc. Apart from these his novels are full in scientific techniques. There are so many scientific concepts in the novel \u27Shiva Triology\u27. There are three parts in Shiva triology. The first part is the immortals of Melutra, the second part is the secret of the Nagas and the third part is the oath of vayuputras. The concept like Radiowaves, manufacture of somras, Divizian of cell etc. are scientifically explained in the novel Shiva triology
Essentials of medical pharmacology / K.D. Tripathi, MD, ex-director-professor and head of Pharmacology, Maulana Azad Medical College and associated LN and GB Pant Hospitals, New Delhi, India.
No full textIncludes bibliographical references (pages 971-973) and index.xvi, 1002 pages
PARTIAL INHIBITION OF MITOCHONDRIAL COMPLEX I ACTIVATES STRESS RESPONSE PATHWAYS INDUCING A PROTECTION AGAINST OXIDATIVE STRESS
No full textWe have previously shown that partial inhibition of mitochondrial complex I activity with a small molecule tricycle pyrone compound (code name CP2) averted the development of cognitive and behavior phenotypes in multiple transgenic mouse models of Alzheimer���s disease (AD). One of the beneficial effects of CP2 involved the protection against oxidative stress in primary mouse neurons, human cells and in mice fed with a high fat diet. In the current study, I investigated the molecular mechanism of CP2-induced neuroprotection and established the translational potential of this therapeutics using murine, human and Drosophila model systems. Target identification revealed that CP2 competes with a flavin mononucleotide (FMN) for the binding to the redox subunit of mitochondrial complex I. Bioenergetics studies showed that CP2 mildly inhibits basal cellular respiration simultaneously leading to a dose-dependent generation of a sub-lethal level of reactive oxygen species (ROS). This increase in ROS rapidly activates cytosolic signaling pathways including the nuclear factor erythroid 2-related factor 2/antioxidant response element (NRF2/ARE) activation to induce a protection against oxidative stress. This retrograde response is known as mitohormesis, and the genetic validation of this phenomenon was done in the longevity studies in several model organisms including Drosophila and C. elegans. Mitohormetic nature of CP2-induced protection against oxidative stress was confirmed using pharmacological and genetic manipulations in human cells, in Drosophila, and in the ARE reporter mice in vivo, and validated in mouse models of the AD. CP2 treatment also reduced the extent of oxidative damage and enhanced the survival in wild-type (WT) mice fed with a high fat diet (HFD), which could be attributed to mitohormetic induction of the NRF2/ARE pathway. In summary, this study provides compelling evidence that mitohormetic activation of the NRF2/ARE pathway using small molecule partial inhibitor of mitochondrial complex I could be beneficial in multiple human conditions where oxidative stress contributes to the disease phenotype
Cracks, microcracks and fracture in polymer structures: Formation, detection, autonomic repair
No full textThe first author would like to acknowledge the financial support from the European Union under the FP7 COFUND Marie Curie Action. N.M.P. is supported by the European Research Council (ERC StG Ideas 2011 n. 279985 BIHSNAM, ERC PoC 2015 n. 693670 SILKENE), and by the EU under the FET Graphene Flagship (WP 14 “Polymer nano-composites” n. 696656)
Kathākāra Nirālā kā prema-darśana
No full textThe theme of love as portrayed in the works of Surya Kant Tripathi, 1896-1961, Hindi author; a stud
Misbeliefs of an Ideal World in Amish Tripathi’s Immortals of Meluha
No full textAmish Tripathi, the bored banker-turned-happy-author of Indian writing in English, has written seven novels till in two series. His novels are famous for his recreation of Indian Hindu mythology and have been sold over seven million copies. The first series Shiva Trilogy deals with Shiva Puranas whereas the second series Ramchandra Series is a fantasy retelling The Ramayana. The concept of Ideal society has been represented by several authors starting from Plato’s Republic to Ursula Le Guin’s The Dispossessed. But, Amish Tripathi is one of the few authors who has created an Ideal world only to show that there can never be an ideal world
Information theory paper data
No full textThis is electrophysiological data of reprogrammed neurons derived from iPSCs of bipolar disorder patients.</p
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