text:
\section{Introduction}

  According to the concordance cosmological model    the universe
experienced
two epochs of accelerated expansion, one at early and one at late times.
Although the latter can be explained by the presence of a cosmological constant,
the related theoretical problem, the possibility of a dynamical behavior, and
especially the inability of the cosmological constant to describe the early
accelerated phase, led to the incorporation of some form of modification.
As a first possibility one can maintain general relativity as the underlying
theory and modify the matter content of the universe by introducing  extra
fields,
such as the
inflaton  at early times
\cite{Olive:1989nu,Bartolo:2004if}  and/or
the dark energy sector at late times
\cite{Copeland:2006wr,Cai:2009zp}.
As a second possibility one modifies the gravitational sector itself,
constructing a theory that  possesses general
relativity
as a particular limit but which in general  exhibits
extra degrees of freedom  \cite{Capozziello:2011et,Cai:2015emx}.

There are many ways to construct gravitational modifications, each one
modifying a particular feature of general relativity. Modifying the
dimensionality  gives rise to the braneworld theories \cite{Brax:2004xh},
modifying the
  Einstein-Hilbert Lagrangian, gives rise to
  $F(R)$ gravity
\cite{DeFelice:2010aj,Nojiri:2010wj},  $F(G)$ gravity
\cite{Nojiri:2005jg,DeFelice:2008wz},   Lovelock theories
\cite{Lovelock:1971yv,Deruelle:1989fj}, etc, while adding a scalar field
coupled with curvature in various ways gives rise to Horndeski/Galileon
theories \cite{Horndeski:1974wa,Nicolis:2008in,Deffayet:2009wt}. Additionally,
starting from the equivalent, teleparallel, formulation of gravity
\cite{Pereira,Maluf:2013gaa} one can construct modifications using torsional
invariants, such as in  $F(T)$ gravity
\cite{Ferraro:2006jd,Linder:2010py}, in $F(T,T_G)$
gravity \cite{Kofinas:2014owa}, or in scalar-torsion
theories \cite{Geng:2011aj,Hohmann:2018rwf}.
Moreover, one can construct the general class of metric-affine
theories \cite{Hehl:1994ue,BeltranJimenez:2012sz,Tamanini:2012mi},
  which incorporates a general  linear  connection structure, or proceed to the
introduction of  non-linear connections such as in
in Finsler and Finsler-like theories
\cite{Bogoslovsky:1999pp,Mavromatos:2010jt,Kouretsis:2012ys,Basilakos:2013hua,
Triantafyllopoulos:2018bli,Ikeda:2019ckp}.

Inspired by these, one could start from such affinely connected metric
theories,
and in particular from their  Riemann-Cartan subclass \cite{Conroy:2017yln},
and construct a theory using a specific but
non-special connection, which would lead to  non-zero torsion and non-zero
curvature at the same time, and thus offering the extra degrees of freedom
typically needed in any gravitational modification \cite{Myrzakulov:2012qp}.
Myrzakulov   gravity can thus lead to a good  phenomenology, being able to
describe the universe evolution at early and late times
\cite{Saridakis:2019qwt,Sharif:2012gz,Momeni:2011am,
Capozziello:2014bna,
Feola:2019zqg}.

One basic question in    modified gravities is the determination of
the arbitrary
function that enters in the theory. Although some general features can be
deduced
through theoretical considerations, such as the absence of ghosts and
 instabilities, or the existence of Noether symmetries,  the most powerful tool
is
the use of   observational data
\cite{Feng:2004ad,Olivares:2005tb,Capozziello:2005pa,Maartens:2006yt,
Lazkoz:2006gp,WoodVasey:2007jb,Zhang:2007sh,Tsujikawa:2007xu,
Basilakos:2009wi,Dutta:2010jh,Nesseris:2010pc,Geng:2011ka,Basilakos:2013nfa,
Basilakos:2015vra,Yang:2018qmz,Anagnostopoulos:2019miu,Pan:2019gop,
Anagnostopoulos:2020ctz,Alfaro:2020dmb,Felegary:2020zuc,
DiValentino:2020vnx}. Hence, in this work we are
interested in using
 expansion data  such as  Supernovae type Ia
data  (SNIa),
Baryonic Acoustic Oscillations (BAO), and Hubble Cosmic Chronometers (CC)
observations, in order to impose constraints on Myrzakulov   gravity.
The plan of the work is the following. In Section \ref{section2} we present
Myrzakulov gravity and its cosmological
applications. In Section
\ref{DataMethodology} we describe the various datasets and  the involved
statistical
methods. Then in Section
\ref{results} we preform our analysis and we present the results, namely the
constraints on the various parameters.
Finally, in  Section
 \ref{Conclusions} we summarize and conclude.

\section{Myrzakulov Gravity and Cosmology}
\label{section2}

In this section we present a brief review of Myrzakulov gravity, or $F(R,T)$
gravity
\cite{Myrzakulov:2012qp,Saridakis:2019qwt}, extracting additionally the
relevant cosmological equations.

\subsection{Myrzakulov Gravity}

The central idea of this modified gravity is
the modification of the underlying connection. In particular, it is known that
imposing a general connection $\omega^{a}_{\,\,\,bc}$ one defines the
 curvature and the torsion tensor respectively
 as \cite{Kofinas:2014owa}
\begin{eqnarray}
&&\!\!\!\!\!\!\!\!\! R^{a}_{\,\,\, b\mu\nu}\!=\omega^{a}_{\,\,\,b\nu,\mu}-
\omega^{a}_{\,\,\,b\mu,\nu}
+\omega^{a}_{\,\,\,c\mu}\omega^{c}_{\,\,\,b\nu}-\omega^{a}_{\,\,\,c\nu}
\omega^{c}_{\,\,\,b\mu}\,,
\label{curvaturebastard}
\end{eqnarray}
\begin{equation}
T^{a}_{\,\,\,\mu\nu}=
e^{a}_{\,\,\,\nu,\mu}-e^{a}_{\,\,\,\mu,\nu}+\omega^{a}_{\,\,\,b\mu}e^{b}_{\,\,\,
\nu}
-\omega^{a}_{\,\,\,b\nu}e^{b}_{\,\,\,\mu}\,,
\label{torsionbastard}
\end{equation}
where $e^{\,\,\, \mu}_a\partial_\mu$ is the tetrad field related to the metric
through  $
g_{\mu\nu} =\eta_{ab}\, e^a_{\,\,\,\mu}  \, e^b_{\,\,\,\nu},
$ where $\ \eta_{ab}=\text{diag}(1,-1,-1,-1)$, with Greek and Latin indices
denoting coordinate and tangent space respectively, and where
comma denotes differentiation.

There are infinite connection choices. The    Levi-Civita
$\Gamma_{abc}$ is the only connection that gives
 vanishing torsion, and from now on we use the label ``LC'' to denote the
 curvature (Riemann) tensor corresponding to $\Gamma_{abc}$, namely
 $R^{(LC)a}_{\,\,\,\ \ \ \ \ \,
b\mu\nu}=\Gamma^{a}_{\,\,\,b\nu,\mu}-
\Gamma^{a}_{\,\,\,b\mu,\nu}
+\Gamma^{a}_{\,\,\,c\mu}\Gamma^{c}_{\,\,\,b\nu}-\Gamma^{a}_{\,\,\,c\nu}
\Gamma^{c}_{\,\,\,b\mu}$.
On the other hand one can use the Weitzenb{\"{o}}ck connection
$W_{\,\,\,\mu\nu}^{\lambda}=e_{a}^{\,\,\,\lambda}e^{a}_{\,\,\,\mu
, \nu } $ which is curvatureless, leading only to torsion as
 $T^{(W)\lambda}_{\,\,\,\ \ \ \ \ \mu\nu}=W^{\lambda}_{\,\,\,\nu\mu}-
W^{\lambda}_{\,\,\,\mu\nu}$
(we use the label ``W'' to denote quantities corresponding to
$W_{\,\,\,\mu\nu}^{\lambda}$.
 From the above it is implied that the Ricci scalar corresponding to the
Levi-Civita connection is
  \begin{eqnarray}
 &&
 \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!
 R^{(LC)}=\eta^{ab} e^{\,\,\, \mu}_a e^{\,\,\, \nu}_b  \left[
 \Gamma^{\lambda}_{\,\,\,\mu\nu,\lambda}
-
 \Gamma^{\lambda}_{\,\,\,\mu\lambda,\nu}
 + \Gamma^{\rho}_{\,\,\,\mu\nu}\Gamma^{\lambda}_{\,\,\,\lambda\rho}
-\Gamma^{\rho}_{\,\,\,\mu\lambda}\Gamma^{\lambda}_{\,\,\,\nu\rho}
  \right],
\end{eqnarray}
while the torsion scalar corresponding to the Weitzenb{\"{o}}ck connection
is
\begin{eqnarray}
&&
\!\!\!\!\!\!\!\!\!\!
T^{(W)}=\frac{1}{4}
\left(W^{\mu\lambda\nu}-
W^{\mu\nu\lambda} \right)
\left(W_{\mu\lambda\nu}  -W_{\mu\nu\lambda}\right)
+\frac{1}{2} \left(W^{
\mu\lambda\nu }
-W^{
\mu\nu\lambda } \right)
\left(W_{\lambda\mu\nu}
-W_{\lambda\nu\mu}\right)
\nonumber\\
&&\ \ \ \ \
- \left(
W_{\nu}^{\,\,\,\mu\nu}
-W_{\nu}^{\,\,\,\nu\mu}\right)
\left( W^{\lambda}_{\,\,\,\mu\lambda}-W^{\lambda}_{\,\,\,\lambda\mu}\right).
\label{TdefW}
 \end{eqnarray}
 As it is known, the former is used in the Lagrangian of General Relativity and
in all curvature-based modified gravities, e.g. in  $F(R)$ gravity
\cite{DeFelice:2010aj}, while the latter is used in the Lagrangian
of teleparallel equivalent of general relativity and in all torsion-modified
gravities, e.g. in $F(T)$ gravity  \cite{Cai:2015emx}.

In  Myrzakulov   gravity one uses a non-special  connection which has  non-zero
curvature and torsion simultaneously \cite{Saridakis:2019qwt}. Hence,   the
resulting theory will in general
possess extra degrees of freedom, even if the imposed Lagrangian is simple,
which is not the case of general relativity or of   teleparallel equivalent
of general relativity that both have two degrees of freedom corresponding to
the
massless graviton. The
  action of the theory is
\begin{equation}
S = \int d^{4}x e \left[ \frac{F(R,T)}{2\kappa^{2}}   +L_m \right],
\label{action1}
\end{equation}
where $e = \text{det}(e_{\mu}^a) = \sqrt{-g}$,  $\kappa^2=8\pi G$ is  the
gravitational constant, and where  we have   introduced
the matter Lagrangian $L_m$ too for completeness. Note that   in
the   arbitrary function  $F(R,T)$  the $R$ and $T$ are the curvature and
torsion scalars corresponding
to the   non-special connection used, which read as
\cite{Kofinas:2014owa}
\begin{eqnarray}
&&
 T=\frac{1}{4}T^{\mu\nu\lambda}T_{\mu\nu\lambda}+\frac{1}{2}T^{\mu\nu\lambda}
T_{\lambda\nu\mu}-T_{\nu}^{\,\,\,\nu\mu}T^{\lambda}_{\,\,\,\lambda\mu},
\label{Tdef2}
\\
&&
 R=R^{(LC)}+T-2T_{\nu\,\,\,\,\,\,\,\,;\mu}^{\,\,\,\nu\mu}\,,
 \label{Radef222}
 \end{eqnarray}
where $;$ marks the covariant differentiation with respect to the
Levi-Civita connection. Therefore,  $T$ depends on the tetrad field, its first
derivative and the connection, while $R$ depends on the tetrad and its first
derivative, and on the connection and its first derivative, with an additional
dependence on the second tetrad derivative due to the last term
of (\ref{Radef222}).
Thus, using (\ref{TdefW}),(\ref{Tdef2}),(\ref{Radef222})
we can finally write
\begin{eqnarray}
&&T=T^{(W)}+v,
\label{T1}
\\
&&
R=R^{(LC)} + u,
\label{R1}
\end{eqnarray}
where $v$ is a scalar depending   on the tetrad, its first
derivative and the connection, while $u$ is a scalar   depending on
the   tetrad, its first and second derivatives, and the connection
and its first derivative.

The quantities  $u$ and $v$  quantify the effect of the
specific but non-special imposed connection.
 In the case where this connection becomes the Levi-Civita
one, then $u=0$ and $v=-T^{(W)}$, and the above theory becomes   the
usual $F(R)$ gravity, which  in turn coincides with general relativity under
$F(R)=R$.
On the other hand, in the case where the   connection is the
Weitzenb{\"{o}}ck
one, then we have that $v=0$ and $u=-R^{(LC)}$ and hence the theory coincides
with $F(T)$
gravity,  which in turn becomes the teleparallel equivalent of general
relativity for $F(T)=T$.

 \subsection{Cosmology}

Let us now apply the above into a cosmological framework and extract the
corresponding equations that determine the universe evolution. As it was shown
in \cite{Saridakis:2019qwt}, in order to avoid complications related to the
additional variation in terms of the
connection, it proves convenient to  apply a mini-super-space procedure.
Hence, we apply  the homogeneous and isotropic  flat
Friedmann-Robertson-Walker (FRW) geometry
\begin{eqnarray}
 ds^2= dt^2-a^2(t)\,  \delta_{ij} dx^i dx^j,
 \end{eqnarray}
which corresponds to the tetrad
$e^a_{\,\,\,\mu}={\text
diag}[1,a(t),a(t),a(t)]$,
where $a(t)$ is the scale factor.
In this case one can easily find  that
$R^{(LC)}=6   \left( \frac{\ddot{a}}{a}+  \frac{\dot{a}^{2}}{a^2}\right)$ and
$T^{(W)}=-6 \left(  \frac{\dot{a}^{2}}{a^2} \right)$. Furthermore, we use the
standard replacement $L_m=-\rho_m(a)$
\cite{Paliathanasis:2014iva,Paliathanasis:2015aos,Dimakis:2016mip}.
Lastly, following the discussion on the dependence of $u$ and $v$ above, we
consistently impose that  $u=u(a,\dot{a},\ddot{a})$ and $v=v(a,\dot{a})$.

 In this work we are interested in exploring
 the cosmological behavior that arise purely from the non-special connection of
Myrzakulov gravity. Hence, we focus on the
 simplest case where the involved arbitrary function is trivial, namely
 $F(R,T)=R+\lambda T$ with $\lambda$ a dimensionless parameter (we omit the
coupling coefficient of $R$ since it
can be absorbed into $\kappa^2$). Note that we do not consider an explicit
cosmological constant term in the Lagrangian. Inserting the above
mini-super-space expressions
into the action (\ref{action1}), for this Lagrangian choice  we acquire $S=\int
Ldt$, where
\begin{eqnarray}
&&
\!\!\!\!\!\!\!\!\!\!\!
L=
\frac{3}{\kappa^2}\left[\lambda+1\right]a\dot{a}^{2}-
\frac{ a^{3}}{2\kappa^2}\left[ u(a,\dot{a},\ddot{a})+\lambda
v(a,\dot{a}) \right]
+ a^3  \rho_m(a)
.\label{4.2}
\end{eqnarray}
Extracting the equations of motion for $a$, alongside
the Hamiltonian constraint  $
{\cal H}=\dot{a}\left[\frac{\partial L}{\partial
\dot{a}}- \frac{\partial}{\partial t}\frac{\partial L}{\partial
\ddot{a}}\right]+\ddot{a}\left(\frac{\partial L}{\partial
\ddot{a}}\right)-L=0 $, we finally acquire the Friedmann
equations
\begin{eqnarray}
3H^{2}&=& \kappa^2\left(
\rho_m+\rho_{de} \right)
\label{FR1a}
\\
2\dot{H}+3H^2
&=&  -\kappa^2 \left(p_m+ p_{de}\right),
\label{FR2a}
\end{eqnarray}
where
\begin{eqnarray}
&&
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!
\rho_{de}=\frac{1}{\kappa^2} \left[
\frac{Ha}{2} \left(u_{\dot{a}}+v_{\dot{a}} \lambda\right) -\frac{1}{2}
(u+\lambda v)
+
\frac{a u_{\ddot{a}}}{2}  \left(\dot{H}-2 H^2\right)
-3\lambda H^2\right]
\label{rhoDEa1}\\
&&
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!
p_{de}=
-\frac{1}{\kappa^2}
\left[\frac{Ha}{2} \left(u_{\dot{a}}+v_{\dot{a}}
\lambda\right)
 -\frac{1}{2} (u+ \lambda v)
 -\frac{a}{6}
\left(u_a+\lambda v_a-{\dot{u}_{\dot{a}}}-\lambda
{\dot{v}_{\dot{a}}}\right)\right.\nonumber\\
&& \left. \ \  \ \  \ \  \ \,  \
-\frac{a}{2}\left(\dot{H}+3H^2\right)u_{\ddot{a}}-H a
\dot{u}_{\ddot{a}}
-\frac{a}{6}
\ddot{u}_{\ddot{a}}
-\lambda(2\dot{H}+3H^2)\right],
\label{pDEa1}
\end{eqnarray}
with $H=\frac{\dot{a}}{a}$   the Hubble parameter,  $p_m$   the matter
pressure, and with the subscripts
$a,\dot{a},\ddot{a}$ denoting partial derivatives with respect to this
argument.
Hence, in the theory at hand,
 we
obtain an effective dark energy sector which  arises from the    non-special
connection. Additionally,   given the matter conservation equation
$ \dot{\rho}_m+3H(\rho_m+p_m)=0$
we find
\begin{eqnarray}
 \dot{\rho}_{de}+3H(\rho_{de}+p_{de})=0,
\end{eqnarray}
which implies that
  the effective dark energy  sector is conserved.

 The above    Friedmann equations can efficiently describe the
  late-time acceleration. A first observation is that   in the case
where $\lambda=0$, namely in the case where the Lagrangian is just  the
curvature (nevertheless the non-special connection leads to non-zero torsion
too), and for the choice   $u=c_1 \dot{a}-c_2$, with $c_1$,$c_2$ constants,
then
we have $
 \rho_{de}=-p_{de}=\frac{c_2}{2\kappa^2}\equiv\Lambda$. Hence, the scenario at
hand includes $\Lambda$CDM cosmology as a sub-case, although we have not
considered
an explicit cosmological constant, since the cosmological constant arises
effectively  from the connection structure of the   theory. Thus, we expect
that a realistic model would be a deviation from the above  scenario.

Finally, it proves convenient to introduce the  decceleration parameter as
\begin{equation}
    \label{deccel_func_def}
    q = -1 - \frac{\dot{H}}{H^2},
\end{equation}
which quantifies the cosmic acceleration. Defining additionally the density
parameters $\Omega_m=\kappa^2\rho_m/(3H^2)$ and
$\Omega_{de}=\kappa^2\rho_{de}/(3H^2)$, as well as the equation-of-state
parameters $w_m\equiv p_m/\rho_m$ and $w_{de}\equiv p_{de}/\rho_{de}$, we can
extract the useful expression
\begin{equation}
    \label{deccel_func_def}
    \frac{2q-1}{3} = \Omega_m w_m+\Omega_{de}w_{de}.
\end{equation}
Hence, in the standard case of dust matter, namely for $w_m\approx0$, we obtain
\begin{equation}
    \label{wde11}
 w_{de}= \frac{2q-1}{3(1-\Omega_m)}.
\end{equation}
This expression allows one to find the evolution of the dark energy
equation-of-state
parameter, knowing the solution of the Friedmann equations, or knowing the
observable values of $H(z)$ (where $z$ is the redshift defined through
$1+z=a_0/a$ setting the current value of the scale factor to $a_0=1$).

In the following we will focus to two models which can satisfy these features.

\subsubsection{Model 1}

  Choosing $u=c_1 \dot{a}-c_2$
and $v=c_3\dot{a}-c_4$,  with $c_3$,$c_4$ constants, we obtain
\begin{eqnarray}
3H^{2}&=& \kappa^2\left(
\rho_m+\rho_{de} \right)
\label{FR1a1}
\\
2\dot{H}+3H^2
&=&  -\kappa^2 \left(p_m+ p_{de}\right),
\label{FR2a1}
\end{eqnarray}
with
\begin{eqnarray}
&&\rho_{de}=\frac{1}{\kappa^2} \left[c-3\lambda H^2\right]
\label{rhoDEa}
\\
&&
p_{de}=
-\frac{1}{\kappa^2}
\left[c-\lambda(2\dot{H}+3H^2)\right],
\label{pDEa}
\end{eqnarray}
where $c\equiv c_2+c_4$. Hence, in this scenario the geometrical sector
constitutes an effective dark energy sector with the above energy density and
pressure, and an equation-of-state parameter of the form
\begin{eqnarray}
&&w_{de}=-1+\frac{2\lambda \dot{H}}{c-3\lambda H^2}.
\label{wDEa}
\end{eqnarray}
Interestingly enough, we can see that $w_{de}$ can be both larger or smaller
than -1, and thus the effective dark energy can be quintessence or phantom
like.

This model has two parameters, namely $c,\lambda$, but one of them can be
eliminated using the present value of the matter density parameter
$\Omega_{m0}$ (from now on the subscript ``0'' denotes the current value of a
quantity), since (\ref{FR1a1}) at present gives:
 \begin{eqnarray}
1= \Omega_{m0}+ \frac{c}{3  H_0^2}-\lambda.
\label{FR2a1b}
\end{eqnarray}
Additionally, the deceleration parameter (\ref{deccel_func_def}), using
(\ref{rhoDEa}),(\ref{pDEa}), becomes
\begin{equation}
\label{qz_myrz1}
    q(z) = -1+ \frac{2\Omega_{m0}(1+z)^3}{\Omega_{m0}(1+z)^3 + 2(1 + \lambda -
\Omega_{m0})},
\end{equation}
and thus its value at present is
\begin{equation}
    \label{q_0_myrz1}
    q_0 = -1 + \frac{3  \Omega_{m0}}{2(1+\lambda)}.
\end{equation}
Comparing with the corresponding value of $\Lambda$CDM scenario, namely
$q^{\Lambda}_0 = -1+3\Omega_{m0}/2$, we verify
     that for the special case of $\lambda = 0$ the two scenarios coincide, as
mentioned above.
Finally, note that from relation (\ref{qz_myrz1}) we can calculate the
transition redshit, namely
the redshift in which $q$ transits from posotive to negative and  we have the
onset of acceleration, finding
\begin{eqnarray}
z_{tr}=-1+2^{1/3} (1+\lambda-\Omega_{m0})^{1/3} \Omega_{m0}^{-1/3}.
\label{ztrmod1}
 \end{eqnarray}

\subsubsection{Model 2}

As a second example   let us consider a more general model with  $u=c_1
\frac{\dot{a}}{a}\ln\dot{a}$
and $v=s(a)\dot{a}$, with $s(a)$ an arbitrary function. In this case
(\ref{rhoDEa1}),(\ref{pDEa1}) give
\begin{eqnarray}
3H^{2}&=& \kappa^2\left(
\rho_m+\rho_{de} \right)
\label{FR1a2}
\\
2\dot{H}+3H^2
&=&  -\kappa^2 \left(p_m+ p_{de}\right),
\label{FR2a2}
\end{eqnarray}
with
\begin{eqnarray}
&&\rho_{de}=\frac{1}{\kappa^2} \left[\frac{c_1}{2}H-3\lambda H^2\right]
\label{rhoDEb}
\\
&&
p_{de}=
-\frac{1}{\kappa^2}
\left[\frac{c_1}{2}H+\frac{c_1}{6}\frac{\dot{H}}{H}-\lambda(2\dot{H}+3H^2)\right
] ,
\label{pDEb}
\end{eqnarray}
 while
\begin{eqnarray}
&&w_{de} =-1+\frac{2\lambda
\dot{H}-\frac{c_1}{6}\frac{\dot{H}}{H}}{\frac{c_1}{2}H-3\lambda H^2}.
\label{wDEb}
\end{eqnarray}
Similarly to the previous example, for this case too  $w_{de}$ can be
quintessence-like or
phantom-like.

This model has two parameters, namely $c_1,\lambda$, but one of them can be
eliminated using $\Omega_{m0}$, since (\ref{FR1a1}) at present time leads
to:
 \begin{eqnarray}
1= \Omega_{m0}+ \frac{c_1}{6  H_0}-\lambda.
\label{FR2a1b2}
\end{eqnarray}
The deceleration parameter (\ref{deccel_func_def}) becomes
\begin{equation}
\label{qz_myrz2}
    q(z) = -1 + \frac{\frac{3}{2} \Omega_{m0}(1+z)^3}{3(1-\Omega_{m0} +
\lambda)
+(1+\lambda)^{-1}\left[(1-\Omega_{m0}+\lambda)^2 +
(1+\lambda)(1+z)^3\Omega_{m0}\right]^{1/2}}
\end{equation}
 and its current value is
 \begin{equation}
     \label{q_0_myrz2}
     q_0 = -1 + \frac{\frac{3}{2} \Omega_{m0}}{3(1-\Omega_{m0} + \lambda)
+(1+\lambda)^{-1}\left[(1-\Omega_{m0}+\lambda)^2 +
(1+\lambda)\Omega_{m0}\right]^{1/2}}.
 \end{equation}
Finally, from relation (\ref{qz_myrz2}) we can calculate the transition redshit
as
\begin{eqnarray}
  &&z_{tr}=-1+\frac{6^{1/3}(1+\lambda)^{-1/3}\Omega_{m0}^{-1/3}}{3}\nonumber\\
  &&
 \cdot\Big\{   10+9
\lambda(2+\lambda-\Omega_{m0})-9\Omega_{m0}
\nonumber\\
&&
-
\sqrt{28-36\Omega_{m0}+9[3\lambda (2+\lambda)-4\lambda
\Omega_{m0}+\Omega_{m0}^2]
}
\Big\}^{1/3}.
\label{ztrmod2}
\end{eqnarray}

\section{Data and Methodology}
\label{DataMethodology}

In this section we describe the various datasets that are going to be used
in our analysis, and  also the involved
statistical
methods.
In particular, we will use   data from direct measurements of
the
Hubble parameter,   from Supernovae Type Ia (SNIa), and from Baryonic Acoustic
Oscillations. Finally, we present various information criteria that offer
information  on the quality of the fit.

\subsection{Cosmological probes}

\subsubsection{Direct measurements of the Hubble expansion}

          From the latest $H(z)$ data set compilation available in Ref.
\cite{YuRatra2018}
we use  only  data obtained from  cosmic chronometers (CC). By using
the
differential age of passive evolving galaxies  one can measure the Hubble rate
directly (see e.g. Ref.
\cite{Moresco:2018xdr} and references therein). These galaxies are massive
galaxies  that evolve ``slowly" at certain intervals of the cosmic time, i.e
with small fraction of ``new" stars. A striking advantage of the
differential
age of passive evolving galaxies is that the resulting measurement of the
Hubble
rate
comes without any assumptions for the underlying cosmology, with the exception
of imposed spatial flatness. Our study
incorporates $N=31$
measurements of the Hubble expansion in the redshift range $0.07 \lesssim z
\lesssim 2.0 $.

Here, the corresponding $\chi^2_{H}$ function reads
          \begin{equation}
          \chi^{2}_{H}\left(\phi^{\nu}\right)=
\sum_{i=1}^{N}\frac{\left[H^{obs}_{i}-H_{th}(z_{i};\phi^{\nu})\right]^2}{\sigma_
{i}^2}\,,
          \end{equation}
          where $H^{obs}_{i}$ is the observed Hubble
rate at redshift $z_{i}$ and $\sigma_{i}$ the corresponding uncertainty, while
$\phi^{\nu}$  is the   statistical vector that
contains the free parameters of the  examined model.

\subsubsection{Supernovae Type Ia}

The most common class of cosmological probes is the so-called ``standard"
candles. The latter are   luminous extra-galactic
astrophysical objects with observable features that are independent of the
cosmic
time.
The
most known standard candles and probably the most thoroughly studied are
Supernovae Type Ia (SNIa). In our
analysis we use the most recent SNIa  dataset available, i.e the binned
Pantheon sample of Scolnic et. al. \cite{Scolnic:2017caz}. The full
dataset is   approximated very efficiently with the binned  $N = 40$
data points belonging to the redshift interval $0.01 \lesssim z \lesssim 1.6$.
          The corresponding $\chi^2$ is
          \begin{equation}
          \chi^{2}_{SN Ia}\left(\phi^{\nu+1}\right)={
          \bold
\mu}_{\text{SNIa}}\,
          {\bold C}_{\text{SNIa},\text{cov}}^{-1}\,{\bold
\mu}_{\text{SNIa}}^{T}\,,
          \end{equation}
          where
          ${\bold
\mu}_{\text{\text{SNIa}}}=\{\mu_{1}-\mu_{\text{th}}(z_{1},\phi^{\nu})\,,\,...\,,
\,
  \mu_{N}-\mu_{\text{th}}(z_{N},\phi^{\nu})\}$. The distance modulus reads as
  $\mu_{i} = \mu_{B,i}-\mathcal{M}$, with $\mu_{B,i}$   the apparent maximum
magnitude      for           redshift $z_{i}$. Here,   $\mathcal{M}$
is a hyper-parameter   \cite{Scolnic:2017caz}   that
quantifies uncertainties
of
various
origins, such as astrophysical ones, data-reduction pipeline, etc, and it is
employed instead of the usage of $\alpha, \ \beta$ free parameters,  in the
context of ``BEAMS with Bias Corrections''
method  \cite{Kessler:2016uwi}. The observed distance modulus is  compared with
the
theoretical one, i.e
  \begin{equation}
  \mu_{\text{th}} = 5\log\left(\frac{d_{L}(z;\phi^{\nu})}{\text{Mpc}}\right) +
25\,,
 \end{equation}
with
 \begin{equation}
d_L(z;\phi^{\nu}) = c(1+z)\int_{0}^{z}\frac{dx}{H(x,\phi^{\nu})}
\end{equation}
  the luminosity distance for   flat FRW geometry. It must be noted
that  $\mathcal{M}$ and the normalized Hubble constant $h$ are
degenerate in light of   Pantheon dataset in an intrinsic way, as it is
usual in standard candles. Therefore, one should jointly employ  other
data-sets in order to obtain meaningful information regarding  the present
value  $H_{0}$.

\subsubsection{Baryonic Acoustic Oscillations}

Baryonic Acoustic Oscillations refer to the imprint left by relativistic sound
waves in the early
universe, providing an observable to the late-time large scale structure.
The main idea is to measure the aforementioned scale at different times (i.e
redshifts), and thus obtain $D_A(z)$ and $H(z)$. The
acoustic length scale corresponds to the co-moving distance that the sound
waves could travel until  the recombination $z_{*}$
\cite{Eisenstein:1997ik}, namely
\begin{equation}
    \label{r_s_theor}
    r_d = \int_{z_{*}}^{\infty}\frac{c_{s}(z)}{H(z)}.
\end{equation}
For the concordance model, the sound speed,  $c_{s}$,  is given from an
analytical expression. However, for the models considered here  there is not
such an expression, therefore the scale $r_d$ will be addressed as a free
parameter.
Furthermore, distances of different objects along the line of sight  correspond
to different redshifts and thus   depend on the combination $H(z)r_d$, while
distances
transverse to the line of sight are related with the combination $D_A (z)/r_d$.

Employing large samples of tracers, (i.e galaxies), one can detect by
statistical means the BAO peak, (for details see  \cite{Alam:2020sor} and
references therein). In order to achieve this  it is required to impose an
underlying cosmology, and hence the method is not model independent.
However, the
differences that may infiltrate at the final data products  are
  much less than the statistical errors, and in most cases the data points are
calibrated with the quantity $r_{d,fid}/r_{d}$. In this work we employ the BAOs
data-set used by   \cite{Ryan:2019uor}, that consists of $N = 11$ data
points  in the redshift range
$0.106 \lesssim z \lesssim 2.36$. The relevant $\chi^2$ function   reads as
\begin{equation}
    \label{chisq_BAOS}
    \chi^{2}_{BAO}\left(\phi^{\nu +1} \right) =
\mathbf{s}C^{-1}_{cov}\mathbf{s}^{T} +
\sum_{i=8}^{N}\frac{\left[T(z_i;\phi^{\nu}) - T^{obs}_{i}\right]^2
    }{\sigma_{i}^2},
\end{equation}
with $C^{-1}_{cov}$   the inverse of the covariance matrix  of the first 6
measurements  available at \cite{Ryan:2019uor}. The vector $\mathbf{s}$ has as
elements the $s_{i}$, given as $s_{i} = d_{m} -d^{obs}_{i}r_d/r_{d,fid}$ for
odd i and
$s_{i} = H(z_{i};\phi^{\nu}) - H^{obs}_{i}r_{d,fid}/r_d$ for even i. In all
cases, $r_{d,fid} = 147.78$. Furthermore, for $i \in \{8,9\}$,
$T(z_i;\phi^{\nu})
= D_v(z_{i};\phi^{\nu})$, $ T^{obs}_{i} = D_{v,i}^{obs} r_d/r_{d,fid}$, with
$r_{fid,8} = 148.69 \ Mpc$ and $r_{fid,9} = 147.66 \ Mpc$ respectively. For $i
= 10$, $T(z_i;\phi^{\nu}) = cH(z_i;\phi^{\nu})^{-0.7}
D_m(z_i;\phi^{\nu})^{0.3}/r_d$ and for
$i=11$, $T(z_i;\phi^{\nu}) = cH(z_i;\phi^{\nu})^{-1}r_d$.
Finally, in the expressions above the following quantities have been used
\begin{subequations}
    \begin{equation}
        D_M(z_i;\phi^{\nu}) = \frac{D_{L}(z_i;\phi^{\nu})}{1+z},
    \end{equation}
    \begin{equation}
        D_A(z_i;\phi^{\nu}) = \frac{D_{L}(z_i;\phi^{\nu})}{(1+z)^2},
    \end{equation}
    \begin{equation}
        D_V(z;\phi^\nu) = \left[\frac{cD_A(z;\phi^\nu)^2 \,z
(1+z)^2}{H(z;\phi^\nu)}\right]^{1/3}\,.
    \end{equation}
    \end{subequations}

\subsubsection{Big Bang Nucleosynthesis}

Any cosmological scenario arising from modified gravity should preserve the
standard thermal history of the universe. Hence, a basic and rough condition is
applicable  in the form of an extra prior. Specifically, we
require that the following inequality holds
\cite{Torres:1997sn,Lambiase:2005kb,Barrow:2020kug}
\begin{equation}
    \frac{\left(H_{i}(z_{BBN};\phi^{\nu}) - H_{\Lambda }(z_{BBN};\Omega_{m0})
\right)^2}{H_{\Lambda}(z_{BBN};\Omega_{m0})^2} < 0.1,
\end{equation}
where $z_{BBN} \sim 10^9$. For the fiducial $\Lambda$CDM cosmology, namely
$H_{\Lambda }$, we employ the parameter
values from Planck  \cite{Aghanim:2018eyx}.

\subsubsection{Joint likelihood analysis}

      In order to  obtain the joint constraints on the cosmological parameters
from  the aforementioned cosmological probes,
        we introduce the total likelihood function as
        \begin{equation}
        \mathcal{L}_{\text{tot}}(\phi^{k}) =  \mathcal{L}_{SNIa}\times
\mathcal{L}_{H}\times \mathcal{L}_{BAO}.
        \end{equation}
        It is easy to deduce that relevant  $\chi^2_{\text{tot}}$   is
given as
        \begin{equation}
        \chi_{\text{tot}}^2(\phi^{k}) = \chi^{2}_{SNIa}+ \chi^{2}_{H}  +
\chi^{2}_{BAO}.
        \end{equation}
        The involved statistical vector has $k$ components, i.e. the $\nu$
        parameters of the scenario at hand plus   $\nu_{\text{hyp}}$
hyper-parameters from the imposed datasets, namely $k = \nu +
\nu_{\text{hyp}}$. Hence, the vector containing the free parameters of the
scenaria at hand    is
$\phi^{k} = \{\Omega_{m0},h,\lambda,\mathcal{M},r_{d} \}$. Note however
that from a statistical
point of view     there is no  distinction between the intrinsic
hyper-parameters
of a given dataset and the free parameters of a cosmological scenario.

Finally, for  the likelihood maximization  we use an
affine-invariant
Markov Chain Monte Carlo sampler \cite{AffineInvMCMC}, obtained in
 the  Python package emcee \cite{emcee}. We use 1000
chains (walkers) and 3500
steps (states). As a prior  we employ firstly the conditions $0.0 <
\Omega_{m0}  < 1$, $0.60 < h < 0.90$, $ -19.9 < M < -18.0$, $-0.9 < \lambda <
2.8$, $135 < r_d < 160$, and secondly the BBN constraint described above.
Lastly, the convergence of the MCMC algorithm is verified with
auto-correlation
time implementation, and moreover for completeness the Gelman-Rubin criterion
is calculated.

\subsection{Information Criteria and Model Selection}
\label{AICBIC}

As a last step we present the standard ways in order to   compare a set of
cosmological scenarios, namely we apply  the Akaike Information Criterion (AIC)
\cite{Akaike1974}, the Bayesian Information Criterion (BIC) \cite{Schwarz1978},
and the Deviance
Information Criterion \cite{Spiegelhalter2002}.  Moreover, we
present the standard $\chi^2_{\textrm{min}}/\textrm{dof}$, where ``dof'' stands
for degrees of freedom,  usually defined as the number of the used data
points minus the number of fitted parameters. In our case this gives dof=77.
Nevertheless, $\chi^2_{\textrm{min}}/\textrm{dof}$ should be used for
illustrative purposes, as the degrees of freedom might be ambiguous for
non-linear (in terms of the free parameters) models. \cite{Andrae:2010gh}.

The AIC criterion is based on information theory  and it is an asymptotically
unbiased estimator of the
Kullback-Leibler information.
Under the standard assumption of
Gaussian
errors, the corresponding estimator for the AIC  criterion reads
\cite{Ann2002,Ann2002b}
\begin{equation}
 \text{AIC}=-2\ln(\mathcal{L}_{\text{max}})+2k+
 \frac{2k(k+1)}{N_{\text tot}-k-1}\,,
 \end{equation}
with $\mathcal{L}_{\text{max}}$   the maximum likelihood of the dataset(s)
under consideration and $N_{\text tot}$   the total  data points  number.
It is apparent that for $N_{\text tot} >> 1$ this expression
 gives the original AIC version, namely $\text{AIC}\simeq
-2\ln(\mathcal{L}_{\text{max}})+2k$. As it is discussed in
\cite{Liddle:2007fy}, it is considered as best practise to use the
modified AIC criterion.

The BIC criterion is a Bayesian evidence   estimator, and it is written as
\cite{Ann2002,Ann2002b,Liddle:2007fy}
\begin{equation}
\text{BIC} = -2\ln(\mathcal{L}_{\text{max}})+k \,{\text log}(N_{\text{tot}})\,.
\end{equation}
Finally, the DIC criterion employs both Bayesian statistics
and
information theory concepts \cite{Spiegelhalter2002}, and it is expressed as
\cite{Liddle:2007fy}
\begin{equation}
{\text {DIC}} = D(\overline{\phi^k}) + 2C_{B}.
\end{equation}
The quantity   $C_{B}$ is the  Bayesian complexity
$C_{B} = \overline{D(\phi^k)} - D(\overline{\phi^k})$,
where   overlines imply the standard mean value.
Moreover, $D(\phi^k)$ is the Bayesian Deviation, which can be expressed as
$D(\phi^k) =
-2\ln[\mathcal{L}(\phi^k)]$ in the case of
exponential
class
of
distributions. It is closely related to the number of effective
degrees of freedom  \cite{Spiegelhalter2002}, which  is actually  the
number of parameters that   affect  the fitting. In a less strict
manner, it could be considered as a measure of the ``spread" of the likelihood.

In contrast with AIC and BIC criteria, instead of using just the best fit
likelihood, DIC uses the whole sample. Furthermore, AIC and BIC count and
penalize all the involved parameters, while DIC penalizes only the number of
parameters that  contribute to the fit in an actual way. Finally, an
additional  appealing feature of DIC criterion is that its calculation is
computationally light under the    MCMC samples.

Given a set of scenarios that describe the same class of phenomena, our problem
is to sort the models according to their fitting efficiency in the context of
the available data. We employ the aforementioned  three information
criteria (IC)  and
we calculate the relative difference of the IC value for the given set
of models, $\Delta
\text{IC}_{\text{model}}=\text{IC}_{\text{model}}-\text{IC}_{\text{min}}$,
where the $\text{IC}_{\text{min}}$ is the minimum $\text{IC}$ value inside the
 competing models set.
In order to qualify each model  in terms of its relevant adequacy, we apply
the
Jeffreys scale
\cite{Kass:1995loi}. Specifically,
the condition $\Delta\text{IC}\leq 2$  implies  statistical compatibility
with the most favoured model by the data, while the condition
$2<\Delta\text{IC}<6$ corresponds to middle tension between the two models, and
lastly the condition $\Delta\text{IC}\geq 10$ implies strong tension.

\section{Results}
\label{results}

In this section we proceed to the observational analysis of   Myrzakulov
gravity using the datasets and the methods described above.   Note that the
free parameters of the aforementioned models are
$\Omega_{m0},\ h$ and $\lambda$, while for the case of the concordance cosmology
they are $\Omega_{m0},\ h$.
For convenience we summarize the obtained results   in Table
\ref{tab:Results1}.
Additionally, in Figs. \ref{figmod1} and  \ref{figmod2} we present the
corresponding  contour plots for Model 1 and Model 2 respectively. For
comparison and benchmark we also analyzed the concordance model, namely
$\Lambda$CDM.

\begin{table}[!]
\tabcolsep 4.pt
\vspace{1mm}
\begin{tabular}{cccccccc} \hline \hline
Model & $\Omega_{m0}$ & $h$ & $\lambda $  & $r_{d}$ & $\mathcal{M}$  &
$\chi_{\text{min}}^{2} $&  $\chi^2_{\text{min}}/dof$  \vspace{0.05cm}\\
\hline
\hline
 Mod. 1 & $0.425_{-0.146}^{+0.107}   $ & $0.691_{-0.017}^{+0.016}  $ &
$0.491_{-0.533}^{+0.387}$ & $ 146.20_{-3.41}^{+2.55} $ &$
-19.382_{-0.052}^{+0.051}$
& 61.93& 0.8043 \\

 Mod. 2 & $ 0.339_{-0.122}^{+0.093}  $ & $0.679_{-0.016}^{+0.016}  $ & $
0.537_{-0.550}^{+0.403} $& $146.60 _{-3.44}^{+3.57}$ &$
-19.396_{-0.052}^{+0.051} $ & 63.53 & 0.8251
\\

$\Lambda$CDM & $0.292_{-0.014}^{+0.015}$ & $0.692 _{-0.017}^{+0.017} $& - &
$145.87_{-3.38}^{+3.53}$ & $-19.377
_{-0.052}^{+0.051}$ & 61.73 &  0.7914 \\

\hline\hline
\end{tabular}
\caption[]{Observational constraints and the
corresponding $\chi^{2}_{\text {min}}$, as well as $\chi_{min}^2/dof$
(where
``dof'' stands for degrees of freedom,  in our case dof = 77),
for the two Myrzakulov gravity models,
presented previously, using CC/Pantheon/BAO data-sets. In order to allow
direct comparison, the concordance flat $\Lambda$CDM model is also analyzed,
 giving results very similar with the corresponding ones of
\cite{Cao:2021ldv}.}
\label{tab:Results1}
\end{table}

\begin{figure}[ht]
\includegraphics[scale=0.53]{Mod1.pdf}
\begin{center}
\caption{{\it{The $1\sigma$, $2\sigma$ and $3\sigma$ likelihood contours for
Model 1 of (\ref{rhoDEa}),(\ref{pDEa}), for all possible 2D subsets of the
parameter space
$(\Omega_{m0},h,\lambda,\mathcal{M},r_{d})$. Moreover, we present the mean
parameter
values   within   the $1\sigma$ area of the MCMC chain. We have
performed a joint
analysis of CC+SNIa+BAO  data.}}}
\label{figmod1}
\end{center}
\end{figure}
  \begin{figure} [ht]
\centering\includegraphics[scale=0.53]{Mod2.pdf}
\caption{{\it{The $1\sigma$, $2\sigma$ and $3\sigma$ likelihood contours for
Model 2 of (\ref{rhoDEb}),(\ref{pDEb}), for all possible 2D subsets of the
parameter space
$(\Omega_{m0},h,\lambda,\mathcal{M},r_{d})$. Moreover, we present the mean
parameter
values   within   the $1\sigma$ area of the MCMC chain. We have
performed a joint
analysis of CC+SNIa+BAO data.}}}
\label{figmod2}
\end{figure}

As we can see, according to the combined analysis of CC+SNIa+BAO data
 we acquire  $\sim 1 \sigma$ compatibility in all cases. The
dimensionless parameter $\lambda$ is constrained to an interval around 0, that
includes $\Lambda$CDM paradigm, which was expected since as we discussed above
a realistic modified gravity should be a small deviation from general
relativity. Nevertheless, note that in both Model 1 and Model 2, the
$\lambda$-contours are slightly shifted towards positive values.
We mention that having the likelihood contours for the parameter
$\lambda$ allows us to extract the constraints on the parameter $c$
through  expression (\ref{FR2a1b}) for Model 1 and on the   parameter $c_1$
through (\ref{FR2a1b2}) for
Model 2. In particular, for 1$\sigma$ region for Model 1 we obtain
$c=1.550^{+0.828}_{-0.876}$, while for Model 2 we find
$c_1=4.94^{+2.28}_{-2.75}$.

Concerning the values of $\Omega_{m0}$ we observe that Model 1 gives a rather
large value, due to the degeneracy with $\lambda$, while for Model 2 this is
not the case. Concerning the Hubble constant $h$, for Model 1 we find that
$0.690_{-0.017}^{+0.016}
 $, while for Model 2 we obtain  $0.679_{-0.016}^{+0.016}  $. This implies that
the
obtained values for the
present Hubble parameter $H_0$ are in between the  Planck estimation $H_0=67.36
\pm 0.54$ km/s/Mpc \cite{Aghanim:2018eyx}  and the local estimation
$H_0=73.24 \pm 1.74$ km/s/Mpc \cite{Riess:2016jrr}, although  closer to
the former.  In addition, the extracted $H_0$ value for both models is
consistent with other astrophysical inferences of Hubble constant, i.e $H_0 =
67.4_{-3.2}^{+4.1} \ km s^{-1}Mpc^{-1}$ \cite{Birrer:2020tax},
and  $H_0 = 69.6 \pm 2.5 \ km s^{-1}Mpc^{-1}$  \cite{Freedman:2020dne}.
It is
interesting to note that     results in this range have been supported for
about a decade now, amongst others in
\cite{Chen:2011ab,Rigault:2014kaa,Chen:2016uno,Zhang:2017aqn,
Dhawan:2017ywl,Fernandez-Arenas:2017isq,Blum:2020mgu}.

In order to provide a more complete and transparent picture,
we   use the obtained   allowed
parameter values  in order to extract the resulting
$H(z)$. In Figs. \ref{Hzmod1} and \ref{Hzmod2} we present   the reconstructed
mean
$H(z)/(z+1)$ as a function of the redshift,  alongside the allowed curves for
the
1$\sigma$ allowed model parameters presented above,
for Model 1 and Model 2  respectively.
These graphs are quite similar with the corresponding ones for quintessence
models ($\phi CDM$) of \cite{Farooq:2016zwm}.
 \begin{figure}[!]
\begin{center}
\includegraphics[scale=0.4]{Hzovermodel1.pdf}
\caption{{\it{
The reconstruction of the  $H(z)/(z+1)$ as a function of the redshift for Model
1, arisen
from (\ref{FR1a1}),(\ref{rhoDEa}). We re-sampled the chains produced by emcee
taking 6000 samples,
and we plot all the obtained   curves, alongside   the curve
corresponding to the best fit of the parameters (red curve).
}}}
\label{Hzmod1}
\end{center}
\end{figure}
\begin{figure}[!]
\begin{center}
\includegraphics[scale=0.4]{Hzovermodel2.pdf}
\caption{{\it{
The reconstruction of the  $H(z)/(z+1)$ as a function of the redshift for Model
2, arisen
from (\ref{FR1a2}),(\ref{rhoDEb}). We re-sampled the chains produced by emcee
taking 6000 samples,
and we plot all the obtained   curves, alongside   the curve
corresponding to the best fit of the parameters (red curve).
}}}
\label{Hzmod2}
\end{center}
\end{figure}

 \begin{figure}[ht]
\begin{center}
\includegraphics[scale=0.44]{wde1n.pdf}
\caption{{\it{The reconstruction of the effective dark-energy equation-of-state
parameter $w_{de}(z)$ as a function of the redshift for Model 1 given by
\eqref{wDEa}. We re-sampled the chains produced by emcee  taking 6000 samples,
and we plot all the obtained $w_{de}(z)$ curves, alongside   the curve
corresponding to the best fit of the parameters (red curve).}}}
\label{w_z_plotFor_Ml1}
\end{center}
\end{figure}

As a next step  we  investigate of the evolution of the dark energy
equation-of-state parameter. In particular, having obtained the allowed
parameter values at 1$\sigma$ confidence level, we can use them in order to
extract the resulting $w_{de}(z)$ behavior given by (\ref{wde11}), with the
deceleration parameter given by (\ref{qz_myrz1}) for Model 1 and by
(\ref{qz_myrz2}) for Model 2.

In Fig.  \ref{w_z_plotFor_Ml1}  we depict the reconstructed mean
$w_{de}(z)$ (red curve) for Model 1, alongside the allowed curves for the
1$\sigma$ allowed model parameters presented above. As we observe, the
corresponding behavior is very close to $\Lambda$CDM scenario for every
parameter values. Similarly, in Fig.  \ref{w_z_plotFor_Ml2}  we present the
corresponding graph for Model 2. In this case the scenario resembles
$\Lambda$CDM at low redshifts, however at earlier times the mean
curve, as well as  many of the ``individual'' curves, present a deviation, since
this is allowed by the used datasets.
In  particular, for some parameter choices the dark-energy pressure at a
particular redshift diverges and changes
sign, and thus the $w_{de}(z)$ transits on the other side of the phantom-divide.
Such
 energy conditions violations are common in modified gravity theories, and
actually
they can lead to interesting cosmological phenomenology.
Note   that the observable quantities (the Hubble function and its derivatives,
the density parameters etc) remain
finite. However, we mention that a significant sub-set of the curves, i.e.
  a large region of the parameter space of the model, does not exhibit such a
behavior,
and the individual obtained
curves resemble the  $\Lambda$CDM evolution.

\begin{figure}[ht]
\begin{center}
\includegraphics[scale=0.44]{wde2.pdf}
\caption{{\it{
The reconstruction of the effective dark-energy equation-of-state
parameter $w_{de}(z)$ as a function of the redshift for Model 2 given by
\eqref{wDEb}. We re-sampled the chains produced by emcee  taking 6000 samples,
and we plot all the obtained $w_{de}(z)$ curves, alongside   the curve
corresponding to the best fit of the parameters (red curve).  The
over-populated
area at the bottom corresponds to a peak within 1$\sigma$ area, nevertheless
since we extract the median value of each parameter within 1$\sigma$   as
the best fit, the  ``best''  $w_{de}(z)$ curve differs.}}}
\label{w_z_plotFor_Ml2}
\end{center}
\end{figure}

Furthermore,  we proceed to the reconstruction of the decceleration parameter
using random sampling of
the obtained chains. Concerning the current value $q_0$,
for Model 1 using
\eqref{q_0_myrz1}  we obtain $q_0 =
-0.561_{-0.021}^{+0.022} $, while for Model 2 using \eqref{q_0_myrz2}
we acquire $q_0 = -0.880_{-0.009}^{+0.010}$. These are in   agreement
with the   values obtained using other datasets, such as supernovae, quasars and
gamma-ray bursts   by means of model-independent techniques
\cite{Rezaei:2020lfy}.

 Additionally, we calculate the transition redshift,  for the two
models, using relations
  (\ref{ztrmod1}) and  (\ref{ztrmod2}) respectively.
 For Model 1 we find $z_{\textrm{tr},1}=0.36_{-0.18}^{+0.10}$, while
 for Model 2 we acquire $z_{\textrm{tr},2}=0.74_{-0.14}^{+0.07}$.
 It is of interest to compare the aforementioned values with $z_{\textrm{tr},A}
= 0.72 \pm 0.05$,
 \cite{Farooq:2016zwm} and $z_{\textrm{tr},B} =
0.64^{+0.12}_{-0.09}$, \cite{Haridasu:2018gqm}.
For Model 1   we observe mild compatibility within $\sim 3.5\sigma$ and within
$\sim 3\sigma$ with ``A'' and ``B'' results, respectively. On the other hand,
for the case of Model 2  we report 1 $\sigma$ compatibility  with both results.
These results act as an additional verification check of the examined models.

We close this analysis with the examination of
 the statistical significance of our fitting
results, applying the AIC, BIC and DIC information criteria described in
subsection \ref{AICBIC}. We summarize our
 results in Table \ref{tab:Results2}. As we observe,   Model 1 is statistically
equivalent with $\Lambda$CDM paradigm, and especially the combined and more
complete  DIC criterion gives an almost equal value. Additionally, Model 2 also
presents  a very good fitting behavior, and according to DIC it is also
statistically equivalent with $\Lambda$CDM paradigm, which is an interesting
result since Model 2 does not contain $\Lambda$CDM scenario as a limit for any
parameter value.
\begin{table}[ht]
\begin{center}
\tabcolsep 4.0pt
\vspace{1mm}
\begin{tabular}{ccccccc} \hline \hline
Model & AIC & $\Delta$AIC & BIC &$\Delta$BIC & DIC & $\Delta$DIC
 \vspace{0.05cm}\\ \hline
\hline
 Mod. 1 & 72.7234 & 2.4757 & 83.9675  & 4.6124 & 69.6728 & 0.0007 \\
Mod. 2 & 74.3204  & 4.0727 &85.5645 & 6.2094 & 71.3725  & 1.7004 \\
$\Lambda$CDM & 70.2477  & 0 & 79.3551 & 0 & 69.6721  & 0  \\
\hline\hline
\end{tabular}
\caption{The information criteria
AIC, BIC and DIC for the examined cosmological models, alongside
the relative difference from the best-fitted model $\Delta\text{IC}
\equiv \text{IC} - \text{IC}_{\text{min}}$.
\label{tab:Results2}}
\end{center}
\end{table}

\section{Conclusions}
\label{Conclusions}

In this work we have used observational data from Supernovae (SNIa) Pantheon
sample, from Baryonic Acoustic Oscillations (BAO), and from cosmic chronometers
  measurements of the Hubble parameter   (CC), alongside arguments from Big
Bang Nucleosynthesis (BBN), in order to extract
constraints on  Myrzakulov $F(R,T)$ gravity. This is a connection-based theory
belonging to the  Riemann-Cartan subclass,
that uses a specific but non-special
connection, which then leads to  extra degrees
of freedom. One introduces a parametrization
  that quantifies the deviation of torsion and curvature    scalars
form their   values corresponding to the special Levi-Civita
and Weitzenb{\"{o}}ck  connections, and then constructs various models by
assuming specific forms for the involved functions. In all models, one obtains
an effective dark-energy sector of geometrical
origin.

We considered two specific models, which are known to lead to interesting
phenomenology. Our analysis shows that both models are capable of describing
 adequately the imposed datasets, namely  CC+SNIa+BAO ones, obtaining $\sim 1
\sigma$ compatibility in all cases. Concerning Model 1, which includes
$\Lambda$CDM paradigm as a particular limit, we found a relatively large value
for $\Omega_{m0}$ and a value for $h$ in between the Planck and local
estimation,  although  closer to
the former. For the
dimensionless parameter $\lambda$ we found
that it is constrained to an interval around
0, which
corresponds to $\Lambda$CDM scenario, however the
corresponding contours are slightly shifted towards positive values.
In the case of Model 2, we found   smaller $\Omega_{m0}$ and   $h$, while
$\lambda$ is again constrained around 0 with favoured positive values.

 Additionally, we used the obtained posterior distribution of the parameters
at
  1$\sigma$ confidence level, and we reconstructed the  Hubble function as a
function of the redshift.
  As we showed, the obtained graphs for  $H(z)/(z+1)$ are in very good agreement
with observations.
 Furthermore, we  reconstructed the induced dark-energy
equation-of-state parameter as a function of the redshift. As we saw, for Model
1 $w_{de}(z)$ is very close to $\Lambda$CDM scenario, while  for  Model 2 it
resembles  $\Lambda$CDM at low redshifts, however at earlier times
 deviations  are  allowed.

  Finally,   applying the AIC, BIC and the combined DIC criteria, we deduced
that both Model 1 and Model 2 present   a very efficient fitting behavior, and
are statistically equivalent with $\Lambda$CDM cosmology. This is an
interesting result since Model 2 does not contain $\Lambda$CDM scenario as a
limit for any parameter value.

 In summary,  Myrzakulov $F(R,T)$ gravity
is  in agreement with
cosmological data, and   it could serve as a   candidate for the description
of nature. Nevertheless, one should also investigate the theory at the
perturbation level and confront it with perturbation-related data, i.e
$f\sigma_8$. Such an analysis, although  both interesting
and necessary, lies beyond the scope of the present work and it is left for a
future project.

\providecommand{\href}[2]{#2}\begingroup\raggedright

redpajama_set_name: RedPajamaArXiv


text:
Texas CIO Report Calls for New Law Requiring K–12 Schools to Report All Cyber Incidents
Expansion of Digital Signatures, Regional Joint IT Operations for Local, State Agencies Also Proposed
By Kristal Kuykendall
The Texas Department of Information Resources, in its newly released Biennial Performance Report, has asked the state legislature to require Texas school districts to report cybersecurity incidents to its office within a minimum reporting timeframe.
Currently, public schools in Texas are required to notify the Texas Education Agency of cyber incidents that result in unauthorized theft, duplication, transmission, use, or viewing of student information that is "sensitive, protected, or confidential as provided by state or federal law." And the Texas Business and Commerce Code says that includes encrypted data, too, if the threat actor has the decryption key.
But, as the Texas Association of School Board discusses at length in several website guides for districts, neither of those laws explain much beyond that — and neither law requires the TEA to publish or share any accounting of the cyber incidents that are reported by school districts. Historically, the TEA has considered such data to be exempt from Freedom of Information laws.
The BPR, released Nov. 16, also requested legislative action to expand DIR's pilot program with Angelo State University in West Texas that established a Regional Security Operations Center to provide university students with hands-on cybersecurity experience and give boots-on-the-ground support to local taxpayer-funded agencies — including K–12 school districts — that need assistance with major cybersecurity incidents.
The BPR tracks state-funded agencies' technology progress in fiscal years 2021 and 2022; highlights their technology accomplishments; lists areas of concern; and recommends policy and legislative changes to improve the effectiveness of IT operations at state and taxpayer-funded agencies.
"Over the past two years, state agencies in Texas showed significant progress in delivering secure, innovative technology that makes government more efficient, effective, transparent, and accountable," said Amanda Crawford, DIR's executive director and Texas' Chief Information Officer, in a statement announcing the report's release. "I applaud the hard work and effort of state agencies which, along with the support of the Texas Legislature, drive the state of Texas to lead the nation in delivering a secure, digital government through well-designed, innovative, and efficient technology solutions."
The 2022 BPR is available on the DIR website at https://dir.texas.gov/strategic-planning-and-reporting/biennial-performance-report.
Other legislative recommendations relevant to public schools included in the new BPR:
Enable private sector peer-to-peer payment solutions commonly used by the public to provide additional payment methods for government services
Enable broader access to digital government services, streamlined processes, and digitization by expanding the use of digital signatures
In discussing the need for better, thorough incident reporting, the BPR states:
"Sharing information is essential for protecting public sector assets, personal or sensitive information, and critical infrastructure. State agencies and institutions of higher education are required to report certain types of security incidents to DIR within a minimum timeframe … suspected cybersecurity incidents, including breaches and ransomware attacks, to DIR. School districts report cybersecurity incidents to the Texas Education Agency and county election officials are required to notify the Secretary of State," the report reads.
"Also, Texas law does not set a standard timeframe for local governments to report cyberattacks. This incongruent reporting of cybersecurity incidents may hinder Texas in tracking trends and understanding the scope and complexity of cyberattacks as well as how they may be related to another cyberattack. By requiring municipalities, school districts, and counties to report cybersecurity incidents to DIR, the state will have a more complete picture of potential threats and may be able to prevent future attacks, avoiding costly response and recovery efforts."
Growing National Push for Mandated, Broader Incident Reporting, Transparency
Nationally, while ransomware attacks even against small school districts usually — eventually — are disclosed either by school leaders, staff members, or the press, there are no federal requirements for public schools to tell anyone about cyberattacks or even breaches of minor students' private information.
Several national cybersecurity nonprofits, private sector risk-management leaders, and education IT professionals have called for greater transparency and accountability from school districts in their cybersecurity efforts — including mandated public disclosure when student or staff data has been breached.
In March, a national nonprofit dedicated to public schools' cybersecurity, K–12 Security Information Exchange, reported statistics showing that ransomware — where a school's student and/or staff data is stolen and a ransom is demanded — has become the most common type of publicly disclosed cyber incident at U.S. schools, but many districts impacted by cyber incidents share little or no information to the community stakeholders affected by those incidents.
K–12 schools are not required to publicly disclose or report cyber incidents, and requirements for vendors to disclose incidents — where mandates exist — are weak and rarely enforced, said K12SIX's State of K–12 Cybersecurity Year in Review report. Vendor data breaches tend to impact scores, if not hundreds, of schools at a time, the report noted, and companies can face fines and lawsuits if they decline to disclose such incidents.
Public K–12 schools, however, are not overseen by any regulations requiring disclosure of cyber incidents or data breaches. Higher education institutions are required to report data breaches of any size, under a 2018 U.S. Department of Education rule affecting any college or university that accepts federal student aid funds.
"There's no question schools should be disclosing these incidents to their communities," K12SIX National Director Doug Levin told THE Journal, when the Year in Review report was released. "Maybe they think they can avoid backlash from the community if they don't disclose a cyber incident. But these schools are spending the community's tax dollars. School board members and those with oversight of the school budget need all the information to do their jobs appropriately, and the community needs to know whether the district's resources are being spent on the right things."
Every public school impacted by a cyber incident should be disclosing basic information such as the fact an incident occurred; who was affected in a potential data breach; the amount of money recovery will cost the district; and recommended steps those affected should take to protect themselves, he argued.
Levin, as national director at K12SIX, is tasked with tracking all publicly disclosed cyberattacks at K–12 schools in the United States. He helps school district IT leaders across the country to improve their protections, and he advocates for more resources and stronger security standards alongside cybersecurity officials at the state and national level as well as with tech companies whose IT and security products are used in public school districts.
He told THE Journal that he has concluded from his many discussions with tech and IT professionals across the K–12 sector that "cyber incidents at K–12 schools are being kept secret all the time" — including incidents where student and staff data has been compromised.
Also earlier this year, SETDA, a national association of U.S. ed tech and IT leaders, released its first Cybersecurity and Privacy Collaborative "landscape scan" calling on federal policymakers and state and local education leaders to work together to increase information sharing and to commit significant, sustained resources and training to improving cybersecurity across the nation's K–12 schools.
California Gov. Gavin Newsom in September signed into a law a new requirement for K–12 schools in that state to report any cyberattack impacting more than 500 pupils or personnel, becoming the first in the nation to require disclosure even if a data breach has not occurred.
Assembly Bill 2355, introduced early this year by Democratic legislator Rudy Salas, requires every California school district, county office of education, or charter school to report to the California Cybersecurity Integration Center any "alteration, deletion, damage, or destruction of a computer system, computer network, computer program, or data caused by unauthorized access" or any "unauthorized denial of access to legitimate users of a computer system, computer network, computer program, or data" if such incident impacts 500 or more students or staff, according to the text of the legislation.
The new California law — which gained final approval from the legislature a week before Los Angeles Unified School District fell victim to a ransomware attack — does not address whether the school cyber incident data will be made public at any point, but it does require Cal-CSIC, the state's cybersecurity oversight agency, to track reports of cyberattacks at K–12 schools and to annually report to the governor and legislature a summary of the cybersecurity incidents reported by the state's public schools.
Levin's advocacy and the K12SIX Year in Review report was cited several times during committee hearings on the California legislation.
"In both of these groups' research, they noted that their findings would be the minimum number of attacks," the California Senate committee report said. "The lack of federal and state reporting requirements means much of the data on cyberattacks are incomplete. There is no archive for cyber-attacks in California. This bill will help ensure schools collect consistent data regarding cyberattacks to ensure further transparency and protection against breaches. There needs to be data and information to begin with so that the scope of attacks can be better understood."
Levin said he hopes the annual reports on the number of cyberattacks targeting public schools will be shared with taxpayers and will lead to the appropriation of more resources to improve schools' cybersecurity posture.
"The devil is in the details of how this will be implemented, but the public has a right to know when these incidents occur so resources are spent appropriately and so districts are held accountable to take the necessary steps to protect themselves from cyber threats," he said.
Additional Legislative Recommendations and Reasoning
The Texas CIO's report hinted at potential help-on-the-way for understaffed K–12 IT and cybersecurity budgets, in its request for state funds to expand the RSOC pilot program:
The law authorizing the RSOC pilot program states the RSOC "may offer network security infrastructure that local governments can utilize and provide real-time network security monitoring; network security alerts; incident response; and cybersecurity educational services. Eligible customers of the RSOC include counties, local governments, school districts, water districts, and hospital districts," according to the BPR summary.
"DIR's vision for the RSOC initiative is to partner with additional public universities and establish RSOCs throughout the state to serve local entities and assist in protecting the state from cyber threats," Crawford wrote in the report. "This vision aligns with a whole-of-state approach to cybersecurity that increases the threat protection and cyber maturity of all of Texas through collaboration and partnerships. DIR is requesting funding from the 88th Legislature to establish two additional RSOCs including one in the Rio Grande Valley and one in central Texas."
Another DIR recommendation that would impact public schools, if lawmakers act, is for new legislation to enable broader access to digital government services, streamlined processes, and digitization by expanding the use of digital signatures.
"Currently, a digital signature can be used to authenticate a written electronic communication sent by an individual to a state agency or local government if the signature complies with DIR's rules as well as rules adopted by the state agency or local government," the BPR explained. "Allowing more digital signatures in lieu of handwritten signatures, without additional rule-making, could lead to improved administrative efficiency and reduced costs."
A final recommendation for lawmakers spelled out in the BPR is "provide guidance for distributed ledger and blockchain technology best practices."
Nationally, a handful of U.S. universities have piloted using blockchain technology to store and share digital credentials such as academic records; although widespread adoption of blockchain for academic records isn't seen as likely in the next year or two, the DIR noted that 10% of state agencies have said they're considering adopting distributed ledger-based systems.
View or download the full 2022 BPR at https://dir.texas.gov/strategic-planning-and-reporting/biennial-performance-report.

redpajama_set_name: RedPajamaCommonCrawl


text:
← Commie Victoria coppers slug free speech activist $68,000 to stop meetings
Telecommunications engineer destroys six mobile phone towers with a tank due to radiation poisoning →
Culleton, Day and Lambie a step closer to being re-instated as Senators
The President of the Senate, Liberal Scott Ryan has been summonsed to appear in the Court of Disputed Returns to defend the unconstitutional referral of Senator Rodney Culleton to the court which saw him dismissed from the senate.
Two weeks ago 'exiled' Senator Rodney Culleton filed an action in the High Court of Australia sitting as the Court of Disputed Returns.
Mr Culleton said his dismissal and that of Senator Bob Day were unconstitutional and that all hostile referrals by the senate of other senators since dismissed were unlawful.
Senator in 'exile' Rod Culleton takes a step closer to being re-instated into the senate
"It is clear that at all material times, the Government did not follow proper due process as required under the Constitution. All referrals from the House post 7th November 2016 appear to be invalid," Mr Culleton told Cairns News.
He said under section 47 of the Commonwealth Constitution of Australia only the senate can decide on the qualifications of a senator.
"On the 4th July 2018, a summons was successfully filed back into the Court of Disputed Returns, Matter No C15/2016 Culleton v Commonwealth.
"This unconcluded case is now unprecedented and has in effect re-opened all invalid hostile referrals that have been invoked by the House under s 376 Commonwealth Electoral Act 1918, post 7th November 2016 which did not comply with the Constitution.
"Section 368 Commonwealth Electoral Act 1918, states Decisions to be final: All decisions of the Court shall be final and conclusive and without appeal, and shall not be questioned in any way.
"Notwithstanding the prohibition as defined in ss 368 and 364 CEA ,Section 47 of the Constitution, in contrast, is squarely addressed to authority to decide and to nothing other than authority to decide. Each House shall be the Judge of the … Qualifications of its own Members", there is in s 47 a textually and Sections 22, 23 and 49 Constitution."
Former Solicitor General for Australia David Bennett AC, QC is acting for Culleton against the Commonwealth
Acting for Mr Culleton is the former Solicitor General of Australia, David Bennett AC, QC who has been following the saga with interest.
Culleton said Mr Bennet believed he had a strong case which was straightforward Constitutional law.
"The relevant effect of the section 47 Constitution is that, unless the Parliament otherwise provides and to the extent that the Parliament does not otherwise provide, 'any question' which answers the description of a 'question respecting the qualification of a senator' in our matters, must be determined by the Senate and not otherwise," stressed Mr Culleton.
"The House must hear the disallowance motion 163 of 2016 and allow all constitutionally elected Senators to appear at the bar in order to have the Senate demonstrate its constitutional commitment of the determination of the identified questions to a coordinated political department as a privy council in order to judge the qualification of its own members.
"This must be remedied to restore honesty and integrity back into Parliament.
"The House is not only sitting unconstitutionally but these breaches have set a bad case precedent in allowing the major parties to re-shuffle the deck of cards and regain power by removing Independents and defanging the minor parties."
Posted on July 23, 2018, in Corporate Government, Courts, Culleton and tagged Bob Day, David Bennett AC, HCA, Jacquie Lambie, QC, senate. Bookmark the permalink.	3 Comments.
Joe Zidar | July 24, 2018 at 12:14 am
Well, I have been following this SAGA with great interest and the ROT in Canberra needs a bloody good and firm kick up the backside.
Lets HOPE that Rod can deliver that KICK with interest.
If my understanding is correct, BRANDIS was also responsible, however, he has done thd runner..
I am still at a lost why we are forced to reference some of these mongrels with "The HONURABLE…"
What an absolute JOKE!!
Rod, may the power of the Constitution all you to return to the Senate
freedomman | July 26, 2018 at 2:15 pm
Keep up the good fight senator this is what this country desperately needs drain the Australian swamp in Canberra and restore constitutional government of by and for the people.
Vicki Rice | August 4, 2018 at 4:35 pm
Good luck , we certainly need to restore a constitutional government for the people of Australia


Rochelle Mann, Professor Emerita at Fort Lewis College, holds degrees from Indiana University and Arizona State University, where her studies included both flute performance and music education. Named FLC's Featured Scholar in 2003, Dr. Mann served as Department Chair for eight of her 24 years as a professor in the Department of Music, and most recently as Acting Dean of the School of Arts, Humanities, and Social Sciences.
Dr. Mann performs frequently as a soloist throughout the Southwest and as Principal Flute with the San Juan Symphony. She has also performed with the Santa Fe Symphony, Aurora Symphony, Four Corners Opera Orchestra, Albuquerque Philharmonic, Showcase Concert Series, Melkus Early Music Ensemble, Animas Chamber Music Festival, Serenata, Santa Fe Desert Chorale, and the Music in the Mountains Festival Orchestra. Her solo and chamber concerts have taken her throughout the United States, Russia, Poland, Estonia, Austria, and France.
A strong advocate for quality music education at every level, Dr. Mann is frequently in international demand as a clinician and guest conductor. She taught public school music in Indiana, Colorado, on the Navajo Reservation in New Mexico, and continues to conduct graduate teacher training workshops throughout the US. After thirteen years as conductor of the Durango Children's Chorale, she now serves as artistic advisor following her retirement in 2009. She is also a program author for the Silver Burdett Making Music K-8 general music series published by Pearson. Her other publications include several works for children's voices as well as articles promoting innovative teaching techniques and performance practice.
Mann can be heard on the following recordings: Raising the Roof - A Celebration of Chamber Music in the Southwest (Artisie4) and Awakening (Equilibrium).


text:
Krav Maga Survival er en moderne Krav Maga (Nærkamp/Selvforsvar) løsning. Krav Maga Survival bygger på eksisterende Krav Maga systemer og en fortløbende udvikling inspireret af bl.a. Hisardut, Kyokushin Karate, MMA, samt erfaringerne fra grundlæggerne af Krav Maga Survival, de mestre der fungerer som tekniske rådgivere, input fra instruktører, elever og eksterne seminarer. Krav Maga Survival bruger aktivt idéen om taktisk overlevelses (Tactical Survival). Krav Maga Survival løsningen bygger på udveksling af teknikker og viden, samt at tage ved lære fra andre nærkamp/selvforsvars løsninger. Krav Maga Survival løsningen består udelukkende af oprejst nærkamp for elevgrader. Løsningen bygger på "KISS" doktrinen – "Keep It Simple – Stupid" og skal altid være enkel at udføre. Målet er, at eleven tilegner sig en effektiv selvforsvars og aktiv nærkamps løsning i løbet af kort tid.

Historie

Inspiration og Oprettelse

Krav Maga Survival blev grundlagt i anerkendelse af de israelske mestre, som kom frem med deres idéer og brugte deres erfaring til at udvikle et succesfuldt system, som gav deres målgruppe et brugbart værktøj. Med Krav Maga som udgangspunkt og inddragelse af teknikker fra andre velfungerende systemer er Krav Maga Survival løsningen blevet til.

Grundstenene til Krav Maga Survival blev lagt i 2005 og det har været en fundamental tanke for grundlæggerne af Krav Maga Survival Shihan Tom "Taiyo" Madsen (6. Dan KMS, 6. Dan IBK Kyokushin, 3. Dan WKA Kickboxing) og Shihan Glenn Jordeim (5. Dan KMS, 5. Dan IBK Kyokushin), at tilpasse teknikkerne, så deres brug ved et givent angreb ikke går ud over, hvad der er forsvarligt i forhold til nødværgeretten. Dette betyder, at Krav Maga Survival løsningen gør brug af proportionalitet ift. situationen. Tilgangen er en hensigtsmæssig adfærd og en proportionel reaktion til et givent angreb under hensyn til angrebets farlighed og angriberens person. Krav Maga Survival organisationen blev en realitet i April 2006.

Taktisk overlevelse (Tactical Survival) er en integreret del af Krav Maga Survival løsningen, som bibringer eleven idéen om altid at have en plan før en potentiel farlig situation opstår, samt hvordan man undgår potentielle farlige situationer.

Målet for Krav Maga Survival løsningen er en fortsat udvikling af de bedste løsninger tilgængelige under betingelserne; realitets baseret – let at lære nærkamp/selvforsvar til professionelle og civile udøvere.

Koncept

Fokus

Den praktiske træning i Krav Maga Survival bruger aktivt Knock Down kamp fra Kyokushin karate og traditionel Boksning som værktøj til at tilegne sig den rette kamp bevægelse og evnen til at modstå det fysiske stress i en nærkamps situation.

Der undervises i strategi og taktik mod en og flere modstandere i forskellige situationer og omgivelser (f.eks. bil, bus, elevator, kontor, bar, fly, demonstrationer)

Krav Maga Survival basis løsning er baseret på stående kampteknikker. Gulvkamp teknikker er en del af instruktør og Mester løsningen.

Fokus på stående kampteknikker skal forstås på baggrund af det faktum, at gulvkamp i en situation uden regler mod flere modstandere kan være ekstremt farlig mod selv "små" modstandere. Selv en let modstander kan give dig et spark i hovedet med fatale konsekvenser og effektivt bruge simple våben som sten og askebægre, når du er immobil på jorden. Ydermere er politi og militær ikke klædt til gulvkamp, idet deres udstyr gør det næsten umuligt at bevæge sig på jorden og rulle rundt uden at pådrage sig skader. Derfor er det essentielt, at eleven intensivt lærer at modstå en modstander, der forsøger at bringe kampen ned på jorden.

Krav Maga Survival eleven vil lære og få viden om:

 Træfpunkter for optimal effekt
 Kritisk situationsgenkendelse
 Kamp under ekstremt pres
 Positionering, timing og kamperfaring
 Modstå ekstrem stress
 Selvforsvar ("Hagana Atsmit")
 Situationskontrol

Løsningen

Krav Maga Survival løsningen består af et antal enkle specificerede teknikker: stande, blokeringer, slag, spark, låse og nedtagninger. Endvidere indbefattes blandt andet teknikker som at nikke en skalde, prik i øjnene, at bide, at kradse, manipulation med små led og ekstreme kontrolgreb.

Løsningen bygger på "KISS" doktrinen – "Keep It Simple – Stupid" og skal altid være enkel at udføre. Målet er at eleven tilegner sig en effektiv selvforsvars og aktiv nærkamps løsning i løbet af kort tid, samt at opbygge en elev der er psykisk og fysisk klar til møde en potentiel farlig situation og om nødvendigt aktivt indgå i nærkamp velforberedt med værktøjer til at løse kritiske situationer både som civil og som professionel.

Alle teknikker er baseret på naturlige reaktioner og fører mod en optimal afslutning med kontrol. Alle løsninger vil blive trænet igen og igen for at sikre den rette reaktion i en stresset situation.

Enhver teknik der ikke er effektiv eller tvivlet på af den tekniske kommission eller Krav Maga Survival sortbælte mestre vil ikke være en officiel del af Krav Maga Survival løsningen.

Instruktører og mestre vil få viden om håndtering og afvæbning af forskellige våben som knive, pistoler og slagvåben. Kontrol med stav og håndjern er tillige indbefattet.

Krav Maga Survival har et bælte gradueringssystem, hvormed elever kan se, hvor de står og holde motivationen. Dette giver således instruktøren mulighed for nøjagtigt at vide, hvilket niveau eleven kan blive presset på for at få maksimal læring.

Krav Maga Survival løsningen er ikke baseret på et håb om medynk fra modstanderen, men vil tvinge eleven til at tage føring og skabe sin egen mulighed for sejr. "Overgivelse er ikke en mulighed."

Tactical Survival

Seks-trins nærkampstaktik:

 Erkend den potentielle farlige situation
 Hold kontakt afstand
 Første kontakt: blokér og omdirigere angrebet
 Angrib samtidigt med trin 3 – skab forvirring
 Kontrollere, passivisere – dette trin er situationsbestemt og afhænger af angrebet farlighed og angriberens person
 Afslut situationen – tilkald politi/ løb væk

Træning

 Fysisk uddannelse og træning
 Teknik træning
 Taktisk træning
 Kamptræning (knock down, Kickboxing, boksning og Krav Maga Survival kamp)
 Slagpuder/sandsæk
 Stress træning og stresshåndtering

Eksterne henvisninger

 Krav Maga Survival International
 Krav Maga Survival Danmark
 IKO Sosai Denmark
 IBK Kyokushin

Kampsport
Selvforsvar

redpajama_set_name: RedPajamaWikipedia


text:
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Check out our video from the release.
A post shared by FieldExtracts (@fieldextracts)
WIZARD TREEZ
A longtime collaborator with Doja Pak and the brain behind Zangria and Mananaz, his work has produced a series of exclusive releases that have set the scene on fire.
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You gotta come up with new strains all the time, and if you collab with other dope brands that have the same vision as you, the sky's the limit.
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A writer, content creator, & event coordinator, Matt Jackson is a polymath whose been working with cannabis for almost two decades. Check out more of his work.
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text:
Review Essay
After the Vultures: Holbrooke's Bosnia Peace Came Too Late
By Roger Cohen
Roger Cohen covered the Bosnian war for The New York Times and is now one of its Paris correspondents. His latest book, Hearts Grown Brutal: Sagas of Sarajevo, will be published by Random House in the fall.
MORE BY Roger Cohen
In This Review
To End a War: From Sarajevo to Dayton -- and Beyond
By Richard Holbrooke
Random House, 1998, 432 pp. $25.00 Purchase
In May 1995, after more than three years of bloodshed in Bosnia, Richard Holbrooke finally lost it. An ineffectual flurry of NATO bombing against Bosnian Serb positions had led to the Serb seizure of more than 300 U.N. peacekeepers and predictable diplomatic paralysis. Holbrooke's recommendation to the White House was blunt: bombard Bosnian Serb leader Radovan Karadzic's self-styled capital in Pale if his men did not release their hostages within 48 hours. The suggestion -- made from Budapest, where Holbrooke was about to wed the writer Kati Marton -- was met with incredulity in Washington. But as Holbrooke, the Clinton administration's Bosnia envoy, relates in To End a War, he was not joking. "I'm serious," Holbrooke told the State Department, "but now I have to get married."
The incident -- at once grotesque, tragic, and faintly comical -- says much about the former assistant secretary of state for Europe, whose rage for peace helped bring an end to the war, and about the cautious administration he served. It also touches on this memoir's fundamental but generally understated tension: between Holbrooke's espousal of forceful solutions and the hesitations of an American military establishment haunted by "mission creep."
Holbrooke has Bosnia in his blood. Early visits in 1992 to Banja Luka and Sarajevo ensured that the genocidal Serb rampage against the Muslims that year -- the central event of the war -- was no abstraction to him. Unlike the mealy-mouthed majority, he had a memory. So armed, he understood that negotiation was useless without the credible threat of force. The West, he warned, "could not expect the Serbs to be conciliatory at the negotiating table as long as they had experienced nothing but success on the battlefield." Moreover, Holbrooke was comfortable with the sort of improvised theatrics that sometimes makes To End a War a study in Balkan diplomacy as the art of the burlesque. In many respects, Holbrooke's achievement was peace-by-tantrum, and in every respect, he was an unusual figure in Bill Clinton's Washington.
Europe Bosnia & Herzegovina Global Institutions Security U.S. Foreign Policy Defense Policy Clinton Administration NATO
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lovely little handmades: a tutorial~ simple patchwork and stars!
a tutorial~ simple patchwork and stars!
The finished size measures 51 1/2 X 60 inches.
Lets cut our pieces...Cut 120, 3 1/2 inch squares for the patchwork, 49, 6 1/2 X 3 1/2 inch rectangles, 7, 3/12 inch squares of red and pink, 56, 2 1/2 inch squares of red and pink, and then 6, 3 1/2 inch squares of aqua, and 48, 2 1/2 inch squares of aqua. To go faster I cut 4 rows at a time.
For the fussy cutting I use a 3 1/2 inch square (from Joanns), to make it easier to get the images centered.
Lets now make our first block. Stitch 4 squares together.
To make the star part, draw a diagonal line with a pencil or pen on the 2 1/2 inch square. Then place the square on one side of one of you 3 1/2 X 6 1/2 inch pieces. Stitch on the line and then with your rotary cutter, cut a 1/4 inch seam. Press seams open.
Now continue as above and stitch the other side.
Continue and do another 3 1/2 X 6 1/2 inch piece. Then place your 4 pieces out to make your first block.
Stitch your top to pieces together.
Stitch the bottom 2 pieces together and then stitch the top and bottom pieces together to make your first block.
Now we have all our blocks together. It is pretty simple, right!?!
Stitch the quilt top together by sewing the blocks into rows and then your rows together.
Yeah, the quilt top is done!
Now all you have left is to add a 1 1/2 inch white border, your 5 1/2 inch border, then sandwich, quilt and bind your quilt!!
Isn't that fun and easy! I hope you enjoyed the tutorial!
Thank you! I pinned it for future reference!
This is beautiful! Thank you so much for the tutorial.
I actually made a similar quilt from a book but the way you have shown it looks a lot easier! The one I did had me do the 4-patches and then the other parts were done as sashing rather than part of the block. I think I'll do another using your method. thanks for the tutorial!
I pinned you! :) Great tutorial and pretty quilt. I love patchwork and stars.
Thanks for sharing. In the cutting instructions, is 7 3 1/2 inch squares? Your quilt is beautiful!
I work with AllFreeSewing and have been trying to contact you. Please email me if there is a good way to reach you. Thanks!
I'll email you. For future reference, the best way to contact me is through the etsy convo feature. Also, you can email me at sewdeerlyloved@hotmail.com. Though sometimes my email gets a bit backed up.
Love this! I am working on a Radiant Ring quilt right now in the same colors, with the Simple Life print fussy-cut for my centers. Unfortunately, they're 4.5" square which is just a little too big for the print -- I end up losing a lot of the motifs. But I just bought more and cut the ones I like best. :) Thanks for the lovely inspiration -- the colors are amazing -- now I can't wait to get mine finished!
This is such a beautiful quilt and a wonderful tutorial! Just wanted to say too that my parcel of Simple Life fabrics from you has arrived safely across the pond! Thank you so much, Kerri, they are gorgeous!
I absolutely love this! How wonderful would it be in Christmas colors!
Love this quilt, thanks so much for the tutorial!
Wow, Kerri, you are brilliant! I love, love, love this quilt. Thank you so much for the tutorial, I will be making this for sure!
Oh Kerri, I received those darling prints (that I won in your last giveaway). They are THE cutest things! I am so overwhelmed by them. They are by far the best thing I have ever won... EVER! I feel so very blessed. I can NOT wait to use them, but am having a hard time coming up with something "worthy" of them! lol As soon as I do, I will definitely post on flickr and send you pics. Thank you soooo very much!
They are looking so beautiful. Patchwork is my favourite. I will do this for table mats.
Kerri, your quilt is so gorgeous! I love every single thing about it, and your wonderful tutorial too. Just lovely!
I have some questions though : which quantity of fat quarter do I need exactly ? If I buy the bunde of 18, will I have some leftovers ?
Thanks again for your time and your wonderful inspiration !
Great Tutorial and such a beautiful quilt! Do you know the finished size? I would like to make a lap quilt for my mother using your tutorial but can't seem to find what's the size.
Thanks for your help and for sharing so much!
I'd love to know the finished size as well.
Also can you say specifically what you used for your red, pink and aqua.
Thanks! This quilt is seriously so cute!
Love this quilt and I just bought the fat quarter bundle from you. Would like to look for the red, pink and aqua online as well. Do you know what colors/ brand you used for those? Thanks!!
Love the quilt & the tut! Thank you very much. I am going to teach a friend to make this quilt as a 50th wedding anniv present for her parents. Using layer cakes and charms from the Tapestry collection. I am thinking she will need to trim the layer cakes down to 8.5 to have the charms used for the points. Your pics motivate me!
Just purchased the bundle. So excited to make this quilt!
Uuuuaaaaauuuu!!!!!!!!! I love this quilt!!!!!!!! Is wonderful!!!!!!
I would love to have these patchwork quilts for my bed. Because I just love your post. what say????
Beautiful!!! This is the best pattern ever for stars. Thanks for sharing!
Im a patchwork noob but have saved fabric from my daughters dresses and want to make her a quilt as beautiful as this before she leaves home. how do i know if i have enough fabric of each type?Any help welcome!
simple stars and patchwork quilt!
easy double hexagon pillow tutorial!
wallpaper dreams & a winner!


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Home Arts & Entertainment Wireless Broadband Alliance Retains Key Board Members as Adoption of Next Generation Wi-Fi Gathers Pace
Wireless Broadband Alliance Retains Key Board Members as Adoption of Next Generation Wi-Fi Gathers Pace
by Atlanta Business Journal September 3, 2022
written by Atlanta Business Journal September 3, 2022
WBA announces the re-election of JR Wilson (AT&T) and Dr. Derek Peterson (Boingo Wireless) as respective Chair and Co-Chair of the WBA board of directors
London, UK, September 1st 2022: The Wireless Broadband Alliance (WBA) today announced the re-election of its chair and co-chair to the board of directors.
JR Wilson, Vice President of Tower Strategy and Roaming at AT&T, will continue as Chairman of the WBA. Mr. Wilson has served as board chairman since 2012, during which time the WBA has made great strides toward creating a seamless, secure and interoperable Wi-Fi ecosystem. Mr. Wilson is responsible for evolving AT&T's overall tower strategy which includes creating a diverse community of suppliers and tower companies who will help increase market competition, as well as overseeing AT&T's domestic and international roaming relationships.
Dr. Derek Peterson, Chief Technology Officer at Boingo Wireless, also retains his position as Co-Chairman of the WBA. Dr. Peterson has been an active and influential member of the WBA for 10 years, spearheading the adoption of global wireless standards and advocating for technology convergence to make wireless connectivity ubiquitous. Under his leadership, Boingo continues to pioneer the adoption and deployment of the latest wireless network technologies including 5G, private networks, Passpoint, and network virtualization.
In May 2022, the WBA reported that OpenRoaming had surpassed one million global hotspots following the launch of OpenRoaming Release 3. The company also signed its 150th member in December 2021 as Telfonica joined alongside a host of new operator and enterprise members.
Following his re-election as Chairman, Mr. Wilson commented: "The WBA has maintained its commitment to making Wi-Fi a truly interoperable and customer-focused technology. That means growing a diverse network of members and partners from all corners of the technology landscape to work together for the benefit of the industry as a whole. In just the past few years we've seen OpenRoaming begin to increase coverage and capacity for an uninterrupted user experience while opening the door to countless new business opportunities."
Dr. Derek Peterson said of his re-election as Co-Chairman: "WBA's vision for connecting the physical and digital worlds through the best wireless technologies available has driven standards adoption across the wireless landscape. Most central to what the WBA does is making wireless accessible to all, simple to access and ready to fuel future innovations. Mobile network operators, carriers, OEMs, device manufacturers, government entities, cable operators – we're all in this together. The new wireless frontier is at our fingertips and together we are at the cornerstone of influencing tomorrow's converged network."
Tiago Rodrigues, CEO of the Wireless Broadband Alliance, said: "I couldn't be more pleased to congratulate Derek and JR on their re-election to the WBA board. In the space of one and a half years, WBA OpenRoaming has managed to surpass one million hotspots worldwide. That's an incredible achievement, and highlights just how quickly the market has identified the benefits to operators, vendors and, of course, end users. If anything, the arrival of 5G has underscored the need for seamless roaming between Wi-Fi and cellular, and our alliance is driving that solution."
About the Wireless Broadband Alliance
Wireless Broadband Alliance (WBA) is the global organization that connects people with the latest Wi-Fi initiatives. Founded in 2003, the vision of the Wireless Broadband Alliance (WBA) is to drive seamless, interoperable service experiences via Wi-Fi within the global wireless ecosystem. WBA's mission is to enable collaboration between service providers, technology companies, cities, regulators and organizations to achieve that vision. WBA's membership is comprised of major operators, identity providers and leading technology companies across the Wi-Fi ecosystem with the shared vision.
WBA undertakes programs and activities to address business and technical issues, as well as opportunities, for member companies. WBA work areas include standards development, industry guidelines, trials, certification and advocacy. Its key programs include NextGen Wi-Fi, OpenRoaming, 5G, IoT, Testing & Interoperability and Policy & Regulatory Affairs, with member-led Work Groups dedicated to resolving standards and technical issues to promote end-to-end services and accelerate business opportunities.
The WBA Board includes Airties, AT&T, Boingo Wireless, Broadcom, BT, Cisco Systems, Comcast, Deutsche Telekom AG, Intel, Reliance Jio, Turk Telekom and Viasat. For the complete list of current WBA members, click here: https://wballiance.com/join-us/current-members/
Follow Wireless Broadband Alliance:
www.twitter.com/wballiance
http://www.facebook.com/WirelessBroadbandAlliance
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Savusavu weather
Today. Maximum daytime temperature: 27 degrees Celsius; Minimum nighttime temperature: 23 degrees Celsius. Light showers. Sunrise: 05:49; Sunset: 18:48. UV: High;
Light showers.
Friday. Maximum daytime temperature: 27 degrees Celsius; Minimum nighttime temperature: 24 degrees Celsius. Light showers. Sunrise: 05:50; Sunset: 18:48. UV: Extreme;
Saturday. Maximum daytime temperature: 27 degrees Celsius; Minimum nighttime temperature: 23 degrees Celsius. Light showers changing to sunny by late morning. Sunrise: 05:50; Sunset: 18:48. UV: Extreme;
Light showers changing to sunny by late morning.
Sunday. Maximum daytime temperature: 27 degrees Celsius; Minimum nighttime temperature: 23 degrees Celsius. Sunny intervals changing to light showers by late morning. Sunrise: 05:51; Sunset: 18:48. UV: Extreme;
Sunny intervals changing to light showers by late morning.
Monday. Maximum daytime temperature: 27 degrees Celsius; Minimum nighttime temperature: 24 degrees Celsius. Light showers. Sunrise: 05:51; Sunset: 18:48. UV: Extreme;
Tuesday. Maximum daytime temperature: 28 degrees Celsius; Minimum nighttime temperature: 24 degrees Celsius. Light showers changing to sunny intervals in the afternoon. Sunrise: 05:52; Sunset: 18:48. UV: Extreme;
Light showers changing to sunny intervals in the afternoon.
Wednesday. Maximum daytime temperature: 27 degrees Celsius; Minimum nighttime temperature: 24 degrees Celsius. Sunny intervals changing to cloudy in the afternoon. Sunrise: 05:53; Sunset: 18:47. UV: Extreme;
Sunny intervals changing to cloudy in the afternoon.
Thursday. Sunny intervals changing to light showers by late morning. Sunrise: 05:53; Sunset: 18:47. UV: Extreme;
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