176 research outputs found
Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
A novel technique, based on the pseudo-random properties of certain graphs known as expanders, is used to obtain novel simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling, and then regrouping the code coordinates. For any fixed (small) rate, and for a sufficiently large alphabet, the codes thus obtained lie above the Zyablov bound. Using these codes as outer codes in a concatenated scheme, a second asymptotic good construction is obtained which applies to small alphabets (say, GF(2)) as well. Although these concatenated codes lie below the Zyablov bound, they are still superior to previously known explicit constructions in the zero-rate neighborhood
Ramsey-nice families of graphs
For a finite family of fixed graphs let be
the smallest integer for which every -coloring of the edges of the
complete graph yields a monochromatic copy of some . We
say that is -nice if for every graph with
and for every -coloring of there exists a
monochromatic copy of some . It is easy to see that if
contains no forest, then it is not -nice for any . It seems
plausible to conjecture that a (weak) converse holds, namely, for any finite
family of graphs that contains at least one forest, and for all
(or at least for infinitely many values of ),
is -nice. We prove several (modest) results in support of this
conjecture, showing, in particular, that it holds for each of the three
families consisting of two connected graphs with 3 edges each and observing
that it holds for any family containing a forest with at most 2
edges. We also study some related problems and disprove a conjecture by
Aharoni, Charbit and Howard regarding the size of matchings in regular
3-partite 3-uniform hypergraphs.Comment: 20 pages, 2 figure
MPC for Tech Giants (GMPC): Enabling Gulliver and the Lilliputians to Cooperate Amicably
In this work, we introduce the Gulliver multi-party computation model (GMPC).
The GMPC model considers a single highly powerful party, called the server or
Gulliver, that is connected to users over a star topology network
(alternatively formulated as a full network, where the server can block any
message). The users are significantly less powerful than the server, and, in
particular, should have both computation and communication complexities that
are polylogarithmic in . Protocols in the GMPC model should be secure
against malicious adversaries that may corrupt a subset of the users and/or the
server.
Designing protocols in the GMPC model is a delicate task, since users can
only hold information about polylog(n) other users (and, in particular, can
only communicate with polylog(n) other users). In addition, the server can
block any message between any pair of honest parties. Thus, reaching an
agreement becomes a challenging task. Nevertheless, we design generic protocols
in the GMPC model, assuming that at most fraction of the users may
be corrupted (in addition to the server). Our main contribution is a variant of
Feige's committee election protocol [FOCS 1999] that is secure in the GMPC
model. Given this tool we show:
1. Assuming fully homomorphic encryption (FHE), any computationally efficient
function with -size output can be securely
computed in the GMPC model.
2. Any function that can be computed by a circuit of depth,
size, and bounded fan-in and fan-out can be
securely computed in the GMPC model without assuming FHE.
3. In particular, sorting can be securely computed in the GMPC model without
assuming FHE. This has important applications for the shuffle model of
differential privacy, and resolves an open question of Bell et al. [CCS 2020]
Perifiton kao delimična zamena komercijalne hrane u organskom gajenju tilapije u Izraelu
Cena hrane čini jednu od najvećih stavki u tekućim troškovima proizvodnje u akvakulturi. Usled potrebe za korišćenjem samo organskih sastojaka, cena koncentrovane hrane za uzgoj organske ribe je izuzetno visoka. Tokom petogodišnjeg perioda rađeni su eksperimenti kako bi se ispitala mogućnost upotrebe različitih supstrata za indukciju rasta perifitona koji bi služio kao prirodna hrana za tilapiju različite veličine, od mlađi do naprednih uzrasnih stadijuma. Kao supstrat, procenjivan je različit poljoprivredni otpad - plastične cevi, najloni i mreže. Različiti supstrati dali su različite prinose perifitona u zavisnosti od njihove površine (glatka ili hrapava) i boje. Rezultati rasta pokazali su da je ušteda hrane od 40% u naprednim fazama rasta dovela do svega 10% redukcije stope rasta tilapije u odnosu na kontrolna jezera, dok je u mladičnjaku moguće smanjiti količinu koncentrovane hrane do 50% bez ograničenja rasta riba. Ovo smanjenje količine hrane od 30-40% dovelo je do poboljšanja koeficijenta konverzije hrane (FCR) od barem 30% u jezerima sa perifitonom (45% u mladičnjacima).
Zaključak: upotreba supstrata hrapavih površina za indukciju rasta perifitona može pomoći u recikliranju otpadnih materijala i značajno redukovati troškove hrane u organskoj akvakulturi
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