The Chasm at Depth Four, and Tensor Rank : Old results, new insightscseiitgn
Agrawal and Vinay [FOCS 2008] showed how any polynomial size arithmetic circuit can be thought of as a depth four arithmetic circuit of subexponential size. The resulting circuit size in this simulation was more carefully analyzed by Koiran [TCS 2012] and subsequently by Tavenas [MFCS 2013]. We provide a simple proof of this chain of results. We then abstract the main ingredient to apply it to formulas and constant depth circuits, and show more structured depth reductions for them.In an apriori surprising result, Raz [STOC 2010] showed that for any $n$ and $d$, such that $\omega(1) \leq d \leq O(logn/loglogn)$, constructing explicit tensors $T: [n] \rightarrow F$ of high enough rank would imply superpolynomial lower bounds for arithmetic formulas over the field F. Using the additional structure we obtain from our proof of the depth reduction for arithmetic formulas, we give a new and arguably simpler proof of this connection. We also extend this result for homogeneous formulas to show that, in fact, the connection holds for any d such that $\omega(1) \leq d \leq n^{o(1)}$. Joint work with Mrinal Kumar, Ramprasad Saptharishi and V Vinay.
Space-efficient Approximation Scheme for Maximum Matching in Sparse Graphscseiitgn
We present a Logspace Approximation Scheme (LSAS), i.e. an approximation algorithm for maximum matching in planar graphs (not necessarily bipartite) that achieves an approximation ratio arbitrarily close to one, in Logspace This deviates from the well known Baker’s approach for approximation in planar graphs by avoiding the use of distance computation - which is not known to be in Logspace. Our algorithm actually works for any “recursively sparse” graph class which contains a linear size matching.The scheme is based on an LSAS in bounded degree graphs which are not known to be amenable to Baker’s method. We solve the bounded degree case by parallel augmentation of short augmenting paths. Finding a large number of such disjoint paths can, in turn, be reduced to finding a large independent set in a bounded degree graph. This is joint work with Samir Datta and Raghav Kulkarni.
Fluig Webinar #6 - Comece o ano em linha com as novas tendências em BPMFluig
Conheça as formas eficazes de gerir processos nas empresas e sugerir inovações. O presidente da Intranet Portal, Marcus Rossetti, é especialista no assunto e mostra como as soluções fluig permitem otimizar processos, para tornar os negócios mais produtivos.
2. Se creo el primer motor de
calculo automático
A pesar de no ser la primer
computadora da inicio al
desarrollo de la misma
Charles
Babbage
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1822
3. Creo la Z1, la primera
computadora programable
Es el comienzo de
prácticamente de todo lo
que nos rodea ahora.
Konrad
Zuse
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1936
4. Patentaron el “dispositivo de
antretenimiento de tubos de
rayos catodicos”
Es considerado el primer
juego de video
Thomas T.
Goldsmith
Estle Ray
Mahn
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1948
5. Patentó el sistema
tricromatico secuencial que
hacia ppsible ver la
television a color Guilermo
Gonzales
Camarena
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1940
6. Se fundó la compañía
Microsoft
Se comienza la era de las
computadoras Bill Gates
Paul Allen
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1975
7. Se funda la compañía Apple
Se revoluciona el concepto
de la computadora con la
idea de hacerla mas
compacta
Steve Jobs
Stephen
Wozniak
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1976
8. Se lanza la Macintosh 128k,
la primera computadora
personal
Apple
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1984
9. Se empieza la
comercialización del primer
teléfono celular
Matin
Cooper
Motorola
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1984
10. La empresa lanza un servicio
de mensajeria instantanea
llamado MSN Messenger
Se podria considerar el inicio
de las redes sociales
Microsoft
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
1999
11. Se funda Facebook
Da impulso al concepto de
redes sociales, se convierte
en la numero uno por
muchos años
Mark
Zuckerberg
Dustin
Moskovitz
Eduardo
Saverin
Chris Hughes
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
2004
12. Se funda Youtube
Se vuelve el sitio web de
streaming de videos mas
grande del mundo Chad Hurley
Steve Chan
Oscar Gomez Velazquez 1B 5 de Diciembre del
2016
2005
